A UGT1A1 Genotype-Directed Study of Belinostat Pharmacokinetics and Toxicity

Background: High-grade neuroendocrine carcinomas (HGNEC) are cancers that develop in different parts of the body, including the digestive tract, genitals, neck, and head. One drug (belinostat), combined with 2 other drugs (etoposide and cisplatin), is approved to treat HGNEC. But some people may have a gene variant that affects how quickly their body gets rid of the drug; these people may do better with different dosages of belinostat. Objective: To test higher or lower doses of belinostat based on gene variants in people with HGNEC. Eligibility: People aged 18 years and older with HGNEC. Design: Participants will be screened. They will have a physical exam with blood tests. Some blood will be used for genetic testing. They will have imaging scans and a test of their heart function. Samples of tumor tissue may be collected. All 3 study drugs (belinostat, etoposide, cisplatin) are given through a tube attached to a needle inserted into a vein. Treatment will be given in 21-day cycles. For cycles 1 through 6: Participants will come to the clinic for the first 4 days. They will be given all 3 drugs. Imaging scans and other tests will be repeated. Each visit will last 4 to 8 hours. After cycle 6: Participants may continue treatment with belinostat alone. They will come to the clinic for the first 3 days of each cycle. They may continue treatment for up to 5 years if the drug is helping them. Participants will have a follow-up visit 30 days after their last dose of belinostat. Then they will receive follow-up visits by phone or email every 3 to 6 months.

-INCLUSION CRITERIA: 1. Participants must have histologically confirmed diagnosis of Extrapulmonary High-Grade Neuroendocrine Neoplasms (HGNENs) for which there is no known standard therapy capable of extending life expectancy. 2. Age \>= 18 years. 3. Participants with neuroendocrine prostate cancer may continue ongoing LHRH agonist therapy. 4. Participants with bone metastases or hypercalcemia who began intravenous bisphosphonate treatment prior to study entry may continue this treatment while on study. 5. Evaluable (measurable or non-measurable) disease, per RECIST 1.1. 6. ECOG performance status \=3,000/mcL * Hemoglobin \>= 10 g/dL * Absolute neutrophil count (ANC) \>=1,500/mcL * Platelets \>=100,000/mcL * Aspartate aminotransferase (AST) or serum glutamic-oxaloacetic transaminase (SGOT) / Alanine aminotransferase (ALT) or serum glutamic-pyruvic transaminase (SGPT): \