Patients must have a locally advanced and unresectable or metastatic gastroenteropancreatic neuroendocrine carcinoma that is either known or suspected to be of gastrointestinal (GI) origin; primary tumors arising from the lung, gynecologic organs or prostate are not permitted

Patients must have pathologically/histologically confirmed tumor of non-small cell histology

Patients must have a Ki-67 proliferative index of 20-100% OR at least 10 mitotic figures per 10 high powered fields

Patients must have measurable disease by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 criteria; baseline measurements and evaluations of all sites of disease must be obtained within 4 weeks prior to randomization and must be acquired by multiphasic computed tomography (CT) or contrast magnetic resonance imaging (MRI)
* NOTE: positron emission tomography (PET)-CT scans are allowed provided the CT portion of the exam is equivalent to a diagnostic CT scan and includes both oral and IV contrast

Patients may not have had any prior systemic treatment (chemotherapy, targeted therapy, peptide receptor radionuclide therapy [PRRT]); prior palliative radiation is permitted but radiated lesions may not be used for measurement

Patients may not have received any of the protocol agents within 5 years prior to randomization

Any prior surgeries must have been completed at least 4 weeks prior to randomization

Patients must have an Eastern Cooperative Oncology Group (ECOG) performance status of 0-2

Patients may not be receiving any other investigational agents while on study treatment

Patients may not be receiving Coumadin while on treatment; other anticoagulants are allowed

Leukocytes >= 3,000/mm^3 (within less than or equal to 14 days prior to randomization)

Absolute neutrophil count >= 1,500/mm^3 (within less than or equal to 14 days prior to randomization)

Hemoglobin >= 9 g/dL (within less than or equal to 14 days prior to randomization)

Platelets >= 100,000/mm^3 (within less than or equal to 14 days prior to randomization)

Total bilirubin =< institutional upper limit of normal (ULN) or =< 1.5 x institutional ULN (if the patient has liver metastases) (within less than or equal to 14 days prior to randomization)

Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase [SGOT])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT]) =< 2.5 x institutional ULN or (=< 5 x institutional ULN if the patient has liver metastases) (within less than or equal to 14 days prior to randomization)

Serum creatinine =< 1.5 x institutional ULN and creatinine clearance >= 60 ml/min (within less than or equal to 14 days prior to randomization)
* NOTE: creatinine clearance must be calculated using the Cockcroft-Gault equation

Patients must have a life expectancy of >= 12 weeks as determined clinically by the treating physician

Patients with brain metastases (either remote or current) or presence of carcinomatous meningitis are not eligible

Patients with known dihydropyrimidine dehydrogenase (DPD) deficiency will be excluded as the use of capecitabine is contraindicated in these patients

Patients must NOT have active or uncontrolled infection, symptomatic heart failure, unstable angina pectoris, cardiac arrhythmia or a serious psychiatric illness/social situation that would limit compliance with study requirements

Patients with impaired decision making capacity may participate in the study if a legal authorized representative is available to consent

Patients must NOT have a history of allergic reactions attributed to compounds of similar chemical or biochemical composition to cisplatin, carboplatin, etoposide, temozolomide or capecitabine

Patients must NOT have absorption issues that would limit the ability to absorb study agents

Patients with a history of the following within =< 12 months of study entry are not eligible:
* Arterial thromboembolic events
* Unstable angina
* Myocardial Infarction

Patients with symptomatic peripheral vascular disease are not eligible

Patients must NOT have previous or concurrent malignancy; exceptions are made for patients who meet any of the following conditions:
* Non-melanoma skin cancer, in situ cervical cancer, superficial bladder cancer, or breast cancer in situ OR
* Prior malignancy completely excised or removed and patient has been continuously disease free for > 5 years OR
* Prior malignancy cured by non-surgical modalities and patient has been continuously disease free for > 5 years

Women must not be pregnant or breast-feeding due to potential harm to the fetus from cisplatin, carboplatin, etoposide, temozolomide and/or capecitabine
* All females of childbearing potential must have a blood test or urine study within 2 weeks prior to randomization 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: 1) has achieved menarche at some point 2) has not undergone a hysterectomy or bilateral oophorectomy; or 3) 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).

Women of childbearing potential and sexually active males must be strongly advised to use an accepted and effective method of contraception or to abstain from sexual intercourse for the duration of their participation in the study

Patients must be able to swallow pills

Patients must be able to tolerate CT or magnetic resonance (MR) imaging including contrast agents as required for the treatment and the protocol

Patients who are known to have human immunodeficiency virus (HIV) or are on combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with cisplatin, carboplatin, etoposide, temozolomide, and/or capecitabine; in addition, these patients are at increased risk of lethal infections when treated with marrow-suppressive therapy; appropriate studies will be undertaken in patients receiving combination antiretroviral therapy when indicated

PRIMARY OBJECTIVE:
I. To assess the progression free survival (PFS) of platinum (cisplatin or carboplatin) and etoposide versus the PFS of temozolomide and capecitabine in patients with advanced G3 non-small cell gastroenteropancreatic neuroendocrine carcinomas.

SECONDARY OBJECTIVES:
I. To assess the response rate (RR) of platinum (cisplatin or carboplatin) and etoposide versus the RR of temozolomide and capecitabine in patients with advanced G3 non-small cell gastroenteropancreatic neuroendocrine carcinomas.
II. To assess the overall survival (OS) of platinum (cisplatin or carboplatin) and etoposide versus the OS of temozolomide and capecitabine in patients with advanced G3 non-small cell gastroenteropancreatic neuroendocrine carcinomas.
III. To evaluate the toxicities associated with the combination of temozolomide and capecitabine and the combination of platinum (cisplatin or carboplatin) and etoposide, respectively, in patients with advanced G3 non-small cell gastroenteropancreatic neuroendocrine carcinomas.

LABORATORY RESEARCH OBJECTIVES:
I. To assess the impact of each treatment regimen on PFS, RR and OS based on marker Ki-67 index in patients with advanced G3 non-small cell gastroenteropancreatic neuroendocrine carcinomas.
II. To assess the prognostic significance of well differentiated versus poorly differentiated non-small cell gastroenteropancreatic neuroendocrine tumors in relationship to survival and response to treatment.
III. To assess the agreement in Ki-67 status between that reported by institutional pathologist and that reported by central pathology review.

OUTLINE: Patients are randomized to 1 of 2 treatment arms.

ARM A: Patients receive capecitabine orally (PO) twice daily (BID) on days 1-14 and temozolomide PO once daily (QD) on days 10-14. Cycles repeat every 28 days in the absence of disease progression or unacceptable toxicity.

ARM B: Patients receive cisplatin intravenously (IV) on days 1-3 or carboplatin IV on day 1. Patients also receive etoposide IV on days 1-3. Cycles repeat every 21 days in the absence of disease progression or unacceptable toxicity.

After completion of study treatment, patients are followed up at 30 days, then every 3 months for 2 years and then every 6 months for 3 years.