ELIGIBILITY CRITERIA FOR STEP 0 (PRE-REGISTRATION): Patient must have pathologically confirmed non-squamous non-small cell lung carcinoma (NSCLC)

ELIGIBILITY CRITERIA FOR STEP 0 (PRE-REGISTRATION): Patient must have stage IV disease (includes M1a, M1b, or recurrent earlier stage disease), according to the 8th edition of the lung cancer Tumor Node Metastasis (TNM) classification system

ELIGIBILITY CRITERIA FOR STEP 0 (PRE-REGISTRATION): Patient must have predominant non-squamous histology (patients with NSCLC no otherwise specified [NOS] are eligible). Mixed tumors will be categorized by the predominant cell type. If small cell elements are present the patient is ineligible

ELIGIBILITY CRITERIA FOR STEP 0 (PRE-REGISTRATION): Patient’s tumor(s) must be tested and known negative for EGFR tyrosinase kinase inhibitor (TKI) sensitizing mutations (EGFR Exon 19 deletions, L858R, L861Q, G719X) and ALK gene rearrangements (by fluorescence in situ hybridization [FISH], next generation sequencing [NGS], or immunohistochemistry [IHC]) by routine Clinical Laboratory Improvement Act (CLIA)-certified clinical testing methods. Negative circulating tumor deoxyribonucleic acid (DNA) results alone are not acceptable. Prior testing for tumor PD-L1 status is not required

ELIGIBILITY CRITERIA FOR STEP 0 (PRE-REGISTRATION): Patients WITHOUT tumors with known molecular alterations in ROS1, MET, RET, or must have progressed radiographically (per local investigator assessment) following one, but only one, line of platinum-based chemotherapy AND one, but only one, line of prior immunotherapy. Lines of therapy are defined by clinical or radiographic progression. Patients may have received chemotherapy and immunotherapy either concurrently or sequentially in either order. Patient must have received at least 2 prior doses of checkpoint inhibitor therapy in an every 2, 3, or 4 week schedule. No submission of molecular testing is required and patients may be registered for Step 0 then proceed directly to Step 1 screening
OR
Patients with tumors with known molecular alterations in ROS1, MET, and RET must have progressed radiographically (per local investigator clinical assessment) on at least one line of prior chemotherapy or targeted therapy, but there is no limit on number of prior number. Reciept of prior immunotherapy is allowed but not required.
* Known molecular alterations in ROS1 , MET, and RET are defined as below ROS1 gene rearrangement by FISH or DNA analysis. In addition to above requirements, these patients must have progressed on at least one prior ROS1 TKI therapy
* MET exon 14 splice mutations on DNA analysis. In addition to above requirements, prior MET directed TKI therapy is optional
* MET mutations predicted to be sensitive to MET inhibitor. In addition to above requirements, prior MET directed TKI therapy is optional
* High MET amplification by FISH (characterized by a fluorescence in situ hybridization MET/CEP7 ratio of 5 or greater); OR MET amplification by DNA NGS CLIA certified assay. In addition to above requirements, prior MET directed TKI therapy is optional
* RET gene rearrangement by FISH or DNA analysis. In addition to above requirements, prior RET directed TKI therapy is optional
** During Step 0 screening, CLIA reports of the testing results must be submitted via Medidata Rave for central review for instructions. The central review will be performed by the study chair, co-chair, biology co-chair, and/or a delegate to determine that the results indicate a patient’s eligibility for targeted therapy. CLIA reports that contain information pertaining to any of the above mutations will be uploaded to Medidata Rave for central review of documentation for determination of patient eligibility for targeted therapy (Arm T). Central testing of tissue will not be performed. Institutions will be notified of the patient’s eligibility status for Arm T within two (2) business days of submission of the molecular testing reports. Patients with tumors with the above known molecular alterations are eligible for cohort Arm Z following Step 1 eligibility review. Patients without tumors with the above known molecular alterations for randomization to Arm A, B or C following Step 1 eligibility review

ELIGIBILITY CRITERIA FOR STEP 0 (PRE-REGISTRATION): NOTE: Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen (in the opinion of the treating physician) are eligible for this trial

ELIGIBILITY CRITERIA FOR STEP 0 (PRE-REGISTRATION): Patients with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents (such as anthracycline or human epidermal growth factor receptor (HER2)-directed antibody therapy, but not prior checkpoint inhibitor therapy), must have a clinical risk assessment of cardiac function using the New York Heart Association functional classification. To be eligible for this trial, patients must be class 2B or better

ELIGIBILITY CRITERIA FOR STEP 0 (PRE-REGISTRATION): Patient must have Eastern Cooperative Oncology Group (ECOG) performance status 0-1

ELIGIBILITY CRITERIA FOR STEP 1 (RANDOMIZATION/REGISTRATION) FOR ALL TREATMENT ARMS: Patient must have met the eligibility criteria outlined above

ELIGIBILITY CRITERIA FOR STEP 1 (RANDOMIZATION/REGISTRATION) FOR ALL TREATMENT ARMS: Patient must have measurable disease as defined by RECIST version (v) 1.1 criteria. Measurements must be obtained within 4 weeks prior to randomization/registration

ELIGIBILITY CRITERIA FOR STEP 1 (RANDOMIZATION/REGISTRATION) FOR ALL TREATMENT ARMS: Patient must have an anticipated life expectancy greater than 3 months

ELIGIBILITY CRITERIA FOR STEP 1 (RANDOMIZATION/REGISTRATION) FOR ALL TREATMENT ARMS: Any prior chemotherapy (based on administration schedule) must have been completed in greater than or equal to the following times prior to randomization/registration:
* Chemotherapy/targeted oral therapy administered in a daily or weekly schedule must be completed >= 1 week prior to randomization/registration
* Any chemotherapy administered in an every 2 week or greater schedule must be completed >= 2 weeks prior to randomization/registration
* Additionally, patient should be recovered to equal to or less than grade 1 toxicities related to any prior treatment, unless adverse events (AE[s]) are clinically non significant and/or stable on supportive therapy (as determined by the treating physician)

ELIGIBILITY CRITERIA FOR STEP 1 (RANDOMIZATION/REGISTRATION) FOR ALL TREATMENT ARMS: Patient must not have had any prior radiation therapy for bone metastasis within 2 weeks, or any other radiation therapy within 4 weeks prior to randomization/registration

ELIGIBILITY CRITERIA FOR STEP 1 (RANDOMIZATION/REGISTRATION) FOR ALL TREATMENT ARMS: Leukocytes >= 3,000/mcL (obtained within 2 weeks prior to randomization/registration)

ELIGIBILITY CRITERIA FOR STEP 1 (RANDOMIZATION/REGISTRATION) FOR ALL TREATMENT ARMS: Absolute neutrophil count >= 1,500/mcL (obtained within 2 weeks prior to randomization/registration)

ELIGIBILITY CRITERIA FOR STEP 1 (RANDOMIZATION/REGISTRATION) FOR ALL TREATMENT ARMS: Platelets >= 100,000/mcL (obtained within 2 weeks prior to randomization/registration)

ELIGIBILITY CRITERIA FOR STEP 1 (RANDOMIZATION/REGISTRATION) FOR ALL TREATMENT ARMS: Hemoglobin >= 9 g/dL (obtained within 2 weeks prior to randomization/registration)

ELIGIBILITY CRITERIA FOR STEP 1 (RANDOMIZATION/REGISTRATION) FOR ALL TREATMENT ARMS: Total bilirubin =< 1.5 x institutional upper limit of normal (ULN) (obtained within 2 weeks prior to randomization/registration)

ELIGIBILITY CRITERIA FOR STEP 1 (RANDOMIZATION/REGISTRATION) FOR ALL TREATMENT ARMS: Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase [SGOT]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT]) =< 2.5 x ULN (obtained within 2 weeks prior to randomization/registration)

ELIGIBILITY CRITERIA FOR STEP 1 (RANDOMIZATION/REGISTRATION) FOR ALL TREATMENT ARMS: Creatinine =< 1.5 x ULN OR calculated (Cockcroft-Gault formula) or measured creatinine clearance >= 50 mL/min/1.73 m^2 (normalized to body surface area [BSA]) for patients with creatinine levels greater than 1.5 times the institutional normal creatinine =< 1.5 x ULN or creatinine clearance >= 50 ml/min/1.73 m^2 (obtained within 2 weeks prior to randomization/registration)

ELIGIBILITY CRITERIA FOR STEP 1 (RANDOMIZATION/REGISTRATION) FOR ALL TREATMENT ARMS: Women must not be pregnant or breast-feeding due to the unknown effects of cabozantinib and nivolumab on human development and for the potential risk for adverse events in nursing infants with the treatment regimens being used. All females of childbearing potential must have a blood test or urine study within 14 days prior to randomization/registration to rule out pregnancy. A female of childbearing potential is any woman, regardless of sexual orientation or whether they have undergone tubal ligation, who meets the following criteria: 
* Has achieved menarche at some point, 
* Has not undergone a hysterectomy or bilateral oophorectomy; 
* Has not been naturally postmenopausal (amenorrhea following cancer therapy does not rule out childbearing potential) for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months).

ELIGIBILITY CRITERIA FOR STEP 1 (RANDOMIZATION/REGISTRATION) FOR ALL TREATMENT ARMS: Women of childbearing potential and sexually active males must not expect to conceive or father children by using accepted and effective method(s) of contraception or by abstaining from sexual intercourse for the duration of their participation in the study and for up to 7 months after completion of treatment on the study

ELIGIBILITY CRITERIA FOR STEP 1 (RANDOMIZATION/REGISTRATION) FOR ALL TREATMENT ARMS: Clinically significant gastrointestinal bleeding within 6 months prior to randomization/registration

ELIGIBILITY CRITERIA FOR STEP 1 (RANDOMIZATION/REGISTRATION) FOR ALL TREATMENT ARMS: Pulmonary hemorrhage or hemoptysis of >= 0.5 teaspoon (2.5 mL) of red blood within 3 months prior to randomization/registration

ELIGIBILITY CRITERIA FOR STEP 1 (RANDOMIZATION/REGISTRATION) FOR ALL TREATMENT ARMS: Any grade drug induced pneumonitis within 3 months prior to randomization/registration. Prior immune mediated pneumonitis of grade 3 or 4 are not eligible regardless of time window

ELIGIBILITY CRITERIA FOR STEP 1 (RANDOMIZATION/REGISTRATION) FOR ALL TREATMENT ARMS: Current radiographic evidence of cavitating pulmonary lesion(s)

ELIGIBILITY CRITERIA FOR STEP 1 (RANDOMIZATION/REGISTRATION) FOR ALL TREATMENT ARMS: Current radiographic evidence of tumor invading any major blood vessels

ELIGIBILITY CRITERIA FOR STEP 1 (RANDOMIZATION/REGISTRATION) FOR ALL TREATMENT ARMS: Evidence of tumor invading the gastrointestinal (GI) tract (esophagus, stomach, small or large bowel, rectum or anus), or any evidence of endotracheal or mainstem endobronchial tumor within 28 days prior to randomization/registration

ELIGIBILITY CRITERIA FOR STEP 1 (RANDOMIZATION/REGISTRATION) FOR ALL TREATMENT ARMS: Peptic ulcer disease, inflammatory bowel, known malabsorption syndrome, bowel obstruction or gastric outlet obstruction (percutaneous endoscopic gastrostomy [PEG] tube placement) within 3 months prior to randomization/registration

ELIGIBILITY CRITERIA FOR STEP 1 (RANDOMIZATION/REGISTRATION) FOR ALL TREATMENT ARMS: Abdominal fistula, GI perforation, intra-abdominal abscess within 6 months prior to randomization/registration

ELIGIBILITY CRITERIA FOR STEP 1 (RANDOMIZATION/REGISTRATION) FOR ALL TREATMENT ARMS: Grade 3 or greater infection, or infection requiring intravenous systemic treatment within 28 days prior to randomization/registration. Patients should be off antibiotics at the time of randomization/registration

ELIGIBILITY CRITERIA FOR STEP 1 (RANDOMIZATION/REGISTRATION) FOR ALL TREATMENT ARMS: Serious non-healing wound/ulcer/bone fracture within 28 days prior to randomization/registration

ELIGIBILITY CRITERIA FOR STEP 1 (RANDOMIZATION/REGISTRATION) FOR ALL TREATMENT ARMS: History of organ transplant

ELIGIBILITY CRITERIA FOR STEP 1 (RANDOMIZATION/REGISTRATION) FOR ALL TREATMENT ARMS: Concurrent symptomatic untreated hypothyroidism within 7 days prior to randomization/registration

ELIGIBILITY CRITERIA FOR STEP 1 (RANDOMIZATION/REGISTRATION) FOR ALL TREATMENT ARMS: History of major surgery (within 3 months, with wound healing within 28 days, prior to randomization/registration), minor surgery (within 28 days prior to randomization/registration), other minor procedures (within 7 days prior to randomization/registration) or clinically relevant ongoing complications from prior surgery

ELIGIBILITY CRITERIA FOR STEP 1 (RANDOMIZATION/REGISTRATION) FOR ALL TREATMENT ARMS: Concurrent uncontrolled hypertension defined as sustained blood pressure (BP) > 140 mm Hg systolic, or > 90 mm Hg diastolic within 7 days of registration despite optimal antihypertensive treatment

ELIGIBILITY CRITERIA FOR STEP 1 (RANDOMIZATION/REGISTRATION) FOR ALL TREATMENT ARMS: Unstable angina pectoris (within 6 months prior to therapy)

ELIGIBILITY CRITERIA FOR STEP 1 (RANDOMIZATION/REGISTRATION) FOR ALL TREATMENT ARMS: Clinically-significant cardiac arrhythmias (within 6 months prior to therapy)

ELIGIBILITY CRITERIA FOR STEP 1 (RANDOMIZATION/REGISTRATION) FOR ALL TREATMENT ARMS: Stroke (including transient ischemic attack [TIA], or other ischemic event) (within 6 months prior to therapy)

ELIGIBILITY CRITERIA FOR STEP 1 (RANDOMIZATION/REGISTRATION) FOR ALL TREATMENT ARMS: Myocardial infarction (within 6 months prior to therapy)

ELIGIBILITY CRITERIA FOR STEP 1 (RANDOMIZATION/REGISTRATION) FOR ALL TREATMENT ARMS: Thromboembolic event (e.g., deep venous thrombosis, pulmonary embolism) within 6 months before first dose (within 6 months prior to therapy)
* NOTE: Subjects with a diagnosis of deep vein thrombosis (DVT) (but not pulmonary embolism [PE]) within 6 months are allowed if stable, asymptomatic, and treated with low molecular weight heparin (LMWH) for at least 2 weeks before first dose

ELIGIBILITY CRITERIA FOR STEP 1 (RANDOMIZATION/REGISTRATION) FOR ALL TREATMENT ARMS: Patient must not receive concomitant anticoagulation with oral anticoagulants (e.g., warfarin, direct thrombin and Factor Xa inhibitors) or platelet inhibitors (e.g., clopidogrel) within 7 days prior to randomization/registration. Allowed anticoagulants are the following:
* Low-dose aspirin (100 mg PO daily or less) is permitted
* Anticoagulation with therapeutic doses of LMWH is allowed in patients who are on a stable dose of LMWH for at least 6 weeks prior to study randomization/registration, and who have had no clinically significant hemorrhagic complications from the anticoagulation regimen or the tumor within this time period

ELIGIBILITY CRITERIA FOR STEP 1 (RANDOMIZATION/REGISTRATION) FOR ALL TREATMENT ARMS: Patient must not receive concomitant treatment of strong CYP3A4 inducers (e.g., dexamethasone (> 1 mg daily dosing), phenytoin, carbamazepine, rifampin, rifabutin, rifapentine, phenobarbital, and St. John’s Wort) within 7 days prior to randomization/registration

ELIGIBILITY CRITERIA FOR STEP 1 (RANDOMIZATION/REGISTRATION) FOR ALL TREATMENT ARMS: Patient must have corrected QT interval calculated by the Fridericia formula QTc corrected by Fridericia (QTcF) =< 500 ms within 28 days prior to randomization/registration

ELIGIBILITY CRITERIA FOR STEP 1 (RANDOMIZATION/REGISTRATION) FOR ALL TREATMENT ARMS: Patient must be able to swallow tablets

ELIGIBILITY CRITERIA FOR STEP 1 (RANDOMIZATION/REGISTRATION) FOR ALL TREATMENT ARMS: Patient must not be on systemic treatment with corticosteroids (> 10 mg daily prednisone equivalents) or other immunosuppressive medications within 14 days prior to randomization/registration, with the following exceptions:
* Inhaled or topical steroids and adrenal replacement doses =< 10 mg daily prednisone equivalents are permitted in the absence of active autoimmune disease
* Patients are permitted to use topical, ocular, intra-articular, intranasal, and inhalational corticosteroids (with minimal systemic absorption)
* Physiologic replacement doses of systemic corticosteroids are permitted, if < 10 mg/day prednisone equivalents. A brief course of corticosteroids for prophylaxis (e.g., contrast dye allergy) or for treatment of non-autoimmune conditions (e.g., delayed-type hypersensitivity reaction caused by contact allergen) is permitted

ELIGIBILITY CRITERIA FOR STEP 1 (RANDOMIZATION/REGISTRATION) FOR ALL TREATMENT ARMS: Patients with treated brain metastases are eligible if follow-up brain imaging after central nervous system (CNS)-directed therapy shows no evidence of progression

ELIGIBILITY CRITERIA FOR STEP 1 (RANDOMIZATION/REGISTRATION) FOR ALL TREATMENT ARMS: Patients with new or progressive brain metastases (active brain metastases) are eligible if the treating physician determines that immediate CNS specific treatment is not required and is unlikely to be required during the first cycle of study treatment.
* Patient must meet one of the following criteria with respect to brain metastases: Patients with no known brain metastasis must have baseline brain imaging within 12 weeks prior to study randomization/registration not demonstrating brain metastases OR patients with known brain metastases must have baseline brain imaging and completed treatment to all symptomatic brain metastases (with whole brain radiation or radiosurgery; or complete neurosurgical resection >= 3 months prior to randomization/registration) >= 4 weeks prior to randomization/registration. They must be clinically stable. Known leptomeningeal disease is not allowed

ELIGIBILITY CRITERIA FOR STEP 1 (RANDOMIZATION/REGISTRATION) FOR ALL TREATMENT ARMS: Patient must not have known active autoimmune disease or known history of autoimmune disease for which recurrence may affect vital organ function or require immune suppressive treatment including systemic corticosteroids (e.g., immune-related neurologic disease, multiple sclerosis, autoimmune neuropathy, Guillain-Barre syndrome, etc.)

ELIGIBILITY CRITERIA FOR STEP 1 (RANDOMIZATION/REGISTRATION) FOR ALL TREATMENT ARMS: Known human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months of registration are eligible for this trial

ELIGIBILITY CRITERIA FOR STEP 1 (RANDOMIZATION/REGISTRATION) FOR ALL TREATMENT ARMS: For patients with known history of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy at time of registration/randomization, if indicated

ELIGIBILITY CRITERIA FOR STEP 1 (RANDOMIZATION/REGISTRATION) FOR ALL TREATMENT ARMS: Patients with a known history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load at time of registration/randomization

ADDITIONAL ELIGIBILITY CRITERIA FOR STEP 1 (RANDOMIZATION) ARMS A-C: Patient must not be eligible for the targeted therapy arm (Arm T) per one of the following criteria:
* Patient was registered on step 0 randomized cohort
* Patient was registered on step 0, targeted cohort however, must meet one of the following criteria:
** Patient did not have a known molecular alteration in ROS1, RET, or MET and did not have central review of tissue
** Central review report the patient is not eligible for Arm T based on molecular report
* Patient was registered on Step 0, targeted cohort however, must meet one of the following criteria:
** Central review results report the patient is not eligible for Arm T
** Central review results report the patient is eligible for Arm T, but patient did not meet the additional eligibility criteria

ADDITIONAL ELIGIBILITY CRITERIA FOR STEP 1 (RANDOMIZATION) ARMS A-C: Patient must not have had any prior anti-MET therapy, such as crizotinib or cabozantinib

ADDITIONAL ELIGIBILITY CRITERIA FOR STEP 1 (RANDOMIZATION) ARMS A-C: Patient must not have had any prior allergic reaction or hypersensitivity to study drug components or related drugs (multitargeted small molecule tyrosine kinase inhibitors or checkpoint inhibitor monoclonal antibodies)

ADDITIONAL ELIGIBILITY CRITERIA FOR STEP 1 (RANDOMIZATION) ARMS A-C: Patients must not have had history of life-threatening toxicity related to prior immune therapy (e.g. anti-PD-1/PD-L1 treatment or any other antibody or drug specifically targeting T-cell co-stimulation or immune checkpoint pathways) except those that are unlikely to re-occur with standard countermeasures (e.g., hypo/hyperthyroidism)

ADDITIONAL ELIGIBILITY CRITERIA FOR STEP 1 (REGISTRATION) TARGETED ARM T: Patient was registered to step 0, targeted arm and central review results report the patient is eligible for arm T

ADDITIONAL ELIGIBILITY CRITERIA FOR STEP 1 (REGISTRATION) TARGETED ARM T: Patients with ROS1 gene rearrangements must have progressed on at least one prior ROS1 targeted therapy such as crizotinib

ADDITIONAL ELIGIBILITY CRITERIA FOR STEP 1 (REGISTRATION) TARGETED ARM T: Patient must have progressed radiographically (per local investigator clinical assessment) on at least one line of prior chemotherapy or targeted therapy, but there is no limit on number of prior number. Prior immunotherapy is allowed but not required. Prior bevacizumab with chemo is allowed.
* NOTE: The requirement for prior chemotherapy will be met if patients have recurrence within 6 months after prior adjuvant platinum based chemotherapy for early stage disease, or recurrence within 6 months after prior radiotherapy plus platinum based chemotherapy for locally advanced disease
* NOTE: Patients with unresectable stage III NSCLC who have received chemo and radiation then consolidation durvalumab, followed by progression are eligible if progression happens after > 2 doses of durvalumab. Prior bevacizumab with chemo is also allowed

STEP 2 ELIGIBILITY CRITERIA (CROSSOVER ARM Z): Patients must have met all eligibility requirements for Step 1 at time of registration to Step 1 to be eligible for Step 2

STEP 2 ELIGIBILITY CRITERIA (CROSSOVER ARM Z): Patients must have radiographic progressive disease per RECIST criteria after >= 2 cycles of therapy on arm C

STEP 2 ELIGIBILITY CRITERIA (CROSSOVER ARM Z): Patients must not have intervening anticancer treatment or major surgical procedure(s) between step 1 and step 2, except palliative radiation to the bone finishing >= 1 week prior to registration to step 2

STEP 2 ELIGIBILITY CRITERIA (CROSSOVER ARM Z): Patients may not have central nervous system progression, but patients with stable CNS disease are allowed

STEP 2 ELIGIBILITY CRITERIA (CROSSOVER ARM Z): Patients must be registered to step 2 within 4 weeks of the last dose of treatment administration from step 1

STEP 2 ELIGIBILITY CRITERIA (CROSSOVER ARM Z): Patients must have an ECOG performance status between 0-2

STEP 2 ELIGIBILITY CRITERIA (CROSSOVER ARM Z): Patients must have recovered to baseline (pre-step 1) or Common Terminology Criteria for Adverse Events (CTCAE) v.5.0 =< grade 1 from toxicity due to all prior therapies except alopecia and other non-clinically significant adverse events (AEs)

STEP 2 ELIGIBILITY CRITERIA (CROSSOVER ARM Z): Leukocytes >= 3,000/mcL (obtained within 2 weeks prior to randomization/registration)

STEP 2 ELIGIBILITY CRITERIA (CROSSOVER ARM Z): Absolute neutrophil count >= 1,500/mcL (obtained within 2 weeks prior to randomization/registration)

STEP 2 ELIGIBILITY CRITERIA (CROSSOVER ARM Z): Platelets >= 100,000/mcL (obtained within 2 weeks prior to randomization/registration)

STEP 2 ELIGIBILITY CRITERIA (CROSSOVER ARM Z): Hemoglobin >= 9 g/dL (obtained within 2 weeks prior to randomization/registration)

Total bilirubin =< 1.5 x institutional ULN (obtained within 2 weeks prior to randomization/registration)

STEP 2 ELIGIBILITY CRITERIA (CROSSOVER ARM Z): Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase [SGOT]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT]) =< 2.5 x ULN (obtained within 2 weeks prior to randomization/registration)

STEP 2 ELIGIBILITY CRITERIA (CROSSOVER ARM Z): Creatinine =< 1.5 x ULN OR calculated (Cockcroft-Gault formula) or measured creatinine clearance >= 50 mL/min/1.73 m^2 (normalized to BSA) for patients with creatinine levels greater than 1.5 times the institutional normal creatinine =< 1.5 x ULN or creatinine clearance >= 50 ml/min/1.73 m^2 (obtained within 2 weeks prior to randomization/registration)

STEP 2 ELIGIBILITY CRITERIA (CROSSOVER ARM Z): Patients must have corrected QT interval calculated by the Fridericia formula (QTcF) =< 500 ms within 28 days before registration

STEP 2 ELIGIBILITY CRITERIA (CROSSOVER ARM Z): No intercurrent illness or disease complication that the investigator believes would limit the ability to safely tolerate the combination of cabozantinib and nivolumab

PRIMARY OBJECTIVE:
I. To determine whether cabozantinib alone, or the combination of nivolumab and cabozantinib, as compared to standard chemotherapy alone, extends progression-free survival (PFS) for this patient population with non squamous NSCLC.

SECONDARY OBJECTIVES:
I. To evaluate the progression free survival (PFS) and best overall radiographic response rate of the targeted therapy arm of the trial.
II. To determine the overall survival for each arm of the trial.
III. To evaluate the best overall radiographic response rate for each arm of the trial.
IV. To evaluate and describe the toxicity profile of monotherapy with cabozantinib, and the combination of nivolumab and cabozantinib in this patient population with non-squamous NSCLC.

EXPLORATORY IMAGING OBJECTIVES:
I. To describe time point tumor response assessment, overall best response, progression-free survival and overall survival using the conventional Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 criteria and the exploratory revised CHOI criteria with all measurements performed by the central review.
II. To compare the progression-free survival using the RECIST1.1 imaging response assessment measurements by site study personnel to those performed by central review.

EXPLORATORY CORRELATIVE OBJECTIVE:
I. To perform correlative biomarker research on tissue and blood biospecimens collected within this trial.

OUTLINE: Patients without known molecular alterations are randomly assigned to 1 of 3 arms. Patients with known molecular alterations are assigned to Arm B.

ARM A: Patients receive cabozantinib S-malate orally (PO) once daily (QD). Cycles repeat every 3 weeks in the absence of disease progression or unacceptable toxicity. Patients may continue to receive therapy after investigator-assessed RECIST 1.1 defined progression, including stable clinical and performance status and have potential for continued clinical benefit.

ARM B: Patients receive cabozantinib S-malate PO QD and nivolumab intravenously (IV) over 30 minutes on day 1. Cycles repeat every 3 weeks in the absence of disease progression or unacceptable toxicity. Patients may continue to receive therapy after investigator-assessed RECIST 1.1 defined progression, including stable clinical and performance status and have potential for continued clinical benefit.

ARM C:
STEP 1: Patients receive ramucirumab IV over 30-60 minutes and docetaxel IV over 1 hour on day 1, or docetaxel IV over 1 hour on day 1 or on days 1 and 8, or gemcitabine hydrochloride IV on days 1 and 8, or paclitaxel IV over 3 hours on day 1, or nab-paclitaxel IV over 30 minutes on days 1, 8, and 15. Cycles repeat every 3 weeks in the absence of disease progression or unacceptable toxicity and at the discretion of the treating physician. Patients may continue to receive therapy after investigator-assessed RECIST 1.1 defined progression, including stable clinical and performance status and have potential for continued clinical benefit.

STEP 2: Patients receive cabozantinib S-malate PO QD and nivolumab IV over 30 minutes on day 1. Cycles repeat every 3 weeks in the absence of disease progression or unacceptable toxicity. Patients may continue to receive therapy after investigator-assessed RECIST 1.1 defined progression, including stable clinical and performance status and have potential for continued clinical benefit.

After the completion of study treatment, patients are followed up every 3 months for up to 3 years.