Patients must be >= 18 years of age

Patients must have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1

Patients must have a general physical condition compatible with the proposed chemotherapy and surgery

Patients must have stage T3 or T4a, histologically-confirmed NPNSCC requiring orbital or skull base resection: (Some patients with T4b disease deemed resectable by the treating surgeon can be included provided they fulfill all other eligibility criteria without involvement of the cavernous sinus

Patients with T4b who have the following characteristics leading to a T4b definition but who in the opinion of the treating surgeon can have resectable disease can be included provided they fulfill all other eligibility criteria and provided they have one of the following presentations: 1. Invasion of orbital apex without involvement of the cavernous sinus 2. Dura invasion depending on extent of involvement and if total resection is deemed feasible. 3. Brain/middle cranial fossa invasion depending on extent of involvement if total resection is deemed feasible. 4. Nasopharynx invasion if very limited 5. Clivus invasion if very limited. (Surgeons are encouraged to consult with the protocol surgical chair for these particular cases). Stages T3 and T4a and selected T4b disease will be included regardless of nodal status (N0 or N1-3), provided that surgical therapy would require orbital or skull base resection. The surgical oncologist in each institution will determine the need for resection of the orbit OR base of skull at baseline for patients on both Arms A and B and following neoadjuvant chemotherapy for patients on Arm B using the score sheet provided at the end of the protocol. 
* Resection of skull base will be deemed necessary according to skull base bone erosion by computed tomography (CT) or marrow involvement by magnetic resonance imaging (MRI) is noted; for any disease abutting the skull base
* Resection of orbital contents will be deemed necessary according to skull base society guidelines, based on involvement of periorbital fat documented by MRI imaging

Patients must be deemed surgically resectable by the surgical teams at each institution and must have a determination of degree of anticipated structure preservation of orbit and skull base; this needs to be determined prior to randomization

Patients may not be receiving investigational agents at time of randomization, or at any time while on study and during the 4 weeks preceding randomization

Patients with a history of allergic reactions attributed to compounds of similar chemical or biologic composition to docetaxel and/or both platinum-based chemotherapy agents are ineligible; patient must be able to receive at least one of the two proposed chemotherapy regimens

Patients with evidence of distant metastases or leptomeningeal disease (LMD) are ineligbile

Patients must not have received previous irradiation for head and neck tumor, skull base, or brain tumors

Patients with uncontrolled inter-current illnesses which in the opinion of the investigator will interfere with the ability to undergo therapy including chemotherapy are ineligbile

Patients with a history of a different malignancy are ineligible, unless the disease has not progressed for >= 2 years

Absolute neutrophil count (ANC) > 1500/mm^3 (=< 2 weeks prior to randomization)

Hemoglobin (Hgb) > 8.0 g/dL (=< 2 weeks prior to randomization)

Platelet count > 100,000/mm^3 (=< 2 weeks prior to randomization)

For patients receiving cisplatin, creatinine clearance must be > 60 ml/min (=< 2 weeks prior to randomization); creatinine clearance may be measured or calculated; if calculating, creatinine clearance, use the Cockcroft-Gault formula

Total bilirubin within 1.5 x the upper limit of normal (ULN) (must be obtained =< 2 weeks prior to randomization)

Aspartate aminotransferase (AST) or alanine aminotransferase (ALT) must be within 1.5 x ULN allowing for eligibility (must be obtained < 2 weeks prior to randomization)

Alkaline phosphatase must be within 1.5 x ULN allowing for eligibility (must be obtained < 2 weeks prior to randomization)

Patients with a prior history of squamous cell or basal carcinoma of the skin or in situ cervical cancer must have been curatively treated

Patient must not have current peripheral neuropathy > grade 2 at time of randomization

Patient must not have any co-existing condition that would preclude full compliance with the study; no prior history of severe hypersensitivity reaction to docetaxel or other drugs formulated with polysorbate 80

Patient must not be pregnant or breast-feeding due to the potential harm to an unborn fetus and possible risk for adverse events in nursing infants with the chemotherapy and radiation being used; in addition, complications from pregnancy may interfere with the ability of patients to have an uninterrupted therapy
* All patients of childbearing potential must have a blood test or urine study within 2 weeks prior to registration to rule out pregnancy
* A patient of childbearing potential is anyone, regardless of sexual orientation or whether they have undergone tubal ligation, who meets the following criteria: 1) has achived menarche at some point, 2) has not undergone a hysterectomy or bilateral oophorectomy; or 3) has not been naturally postmenopausal for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months)

Patient must not be expected conceive or father children by using an accepted and effective method(s) of contraception or by abstain from sexual intercourse for the duration of their participation in the study

Patient must have measurable disease; MRI and/or PET/CT scans need to be performed within 2 weeks prior to randomization

PRIMARY OBJECTIVES:
I. Evaluate the structure preservation rate for patients with locally advanced resectable nasal and paranasal sinus squamous cell carcinoma (NPNSCC) with or without neoadjuvant therapy; all patients will undergo surgical resection and postoperative standard care.
II. Evaluate overall survival (OS) for patients with locally advanced resectable NPNSCC with or without neoadjuvant therapy followed by surgical resection and postoperative standard care.

SECONDARY OBJECTIVES:
I. Evaluate progression-free survival (PFS) for this patient population.
II. Examine the rate of structure preservation for the orbit (freedom from orbital exenteration).
III. Evaluate site reported p16 data and correlate with outcome.
IV. Determine the accuracy of baseline/post-chemotherapy magnetic resonance imaging (MRI) and/or fludeoxyglucose F-18 positron emission tomography/computed tomography (FDG PET/CT)-based prediction of orbit and skull base preservation.
V. Determine the accuracy of baseline/post-chemotherapy MRI and/or FDG PET/CT-based prediction of 2-year overall survival.

EXPLORATORY TOBACCO USE OBJECTIVES:
I. To determine the effects of tobacco, operationalized as combustible tobacco (1a), other forms of tobacco (1b), and environmental tobacco exposure (ETS) (1c) on provider-reported cancer-treatment toxicity (adverse events [both clinical and hematologic] and dose modifications).
II. To determine the effects of tobacco on patient-reported physical symptoms and psychological symptoms.
III. To examine quitting behaviors and behavioral counseling/support and cessation medication utilization.
IV. To explore the effect of tobacco use and exposure on treatment duration, relative dose intensity, and therapeutic benefit.

OUTLINE: Patients are randomized to 1 of 2 arms.

ARM A: Patients undergo standard of care surgery. Beginning 4-6 weeks after surgery, patients undergo image guided intensity modulated radiation therapy (IMRT) once daily (QD) for 5 fractions per week for 30 fractions. Patients with positive margins/positive extracapsular spread (ECS) in lymph nodes undergo image guided IMRT QD for 5 fractions per week for 30 fractions and cisplatin intravenously (IV) over 1-2 hours or carboplatin IV over 30 minutes (for patients who are ineligible to receive cisplatin) weekly for 6 weeks in the absence of disease progression or unacceptable toxicity.

ARM B: Patients receive docetaxel IV over 1 hour and cisplatin IV over 1-2 hours on day 1. Patients who are ineligible to receive cisplatin receive carboplatin IV over 30 minutes on day 1. Treatment repeats every 21 days for up to 3 cycles in the absence of disease progression or unacceptable toxicity. Patients then undergo standard of care surgery no later than 6 weeks following the last dose of chemotherapy. Beginning 4-6 weeks after surgery, patients undergo image guided IMRT QD for 5 fractions per week for 30 fractions. Patients with positive margins/positive ECS in lymph nodes undergo image guided IMRT QD for 5 fractions per week for 30 fractions and cisplatin IV over 1-2 hours or carboplatin IV over 30 minutes (for patients who are ineligible to receive cisplatin) weekly for 6 weeks in the absence of disease progression or unacceptable toxicity.

After completion of study treatment, patients are followed up every 3 months if < 2 years from study entry and then every 6 months if 2-5 years from study entry.