A UGT1A1 Genotype-Directed Study of Belinostat Pharmacokinetics and Toxicity

Background: * Extrapulmonary High-Grade Neuroendocrine Neoplasms (HGNENs) are all high-grade neoplasms that may resemble small cell carcinoma or large cell Neuroendocrine Carcinomas (NEC) of the lung. Poorly differentiated NECs are often associated with a rapidly progressive disease and a proliferative rate (Ki67%) \>20%. * As a general rule, poorly differentiated NECs are treated with platinum-based regimens according to small cell carcinoma guidelines. * This protocol will study a continuous infusion of the histone deacetylase (HDAC) inhibitor belinostat in combination with cisplatin and etoposide for patients with advanced neuroendocrine neoplasms. Objective: -To determine if pharmacogenomic intervention can normalize the area under the curve (AUC) at cycle 6 between UGT1A1\*28 and UGT1A1\*60 genotypes) of belinostat administered as a continuous 48 h infusion in combination with cisplatin and etoposide in participants with neuroendocrine malignancies based on UGT1A1\*28 and UGT1A1\*60 genotypes. Eligibility: * The protocol will be open to participants with Extrapulmonary High-Grade Neuroendocrine Neoplasms (HGNENs) * Participants will be recruited based on genotype, with n=9 carrying UGT1A1\*1/\*1 or UGT1A1\*1/\*28 and n=30 carrying any other combination of variant alleles at UGT1A1\*28 or UGT1A1\*60. * Age \>=18 years * ECOG Performance Status 0-2 Design: * Parallel design in which the starting dose of belinostat is administered as a 48-hour continuous infusion at two possible doses based on genotype: 1) 400mg/m\^2/day for UGT1A1\*28/\*28 or at least one UGT1A1\*60 allele UGT1A1\*28 and UGT1A1\*60 genotypes or 2) 600 mg/m\^2/day for wild-type participants and those carrying UGT1A1\*1/\*28 in the absence of other variant alleles. * To define pharmacokinetics, toxicities of belinostat provided to participants who carry the above genotype groups. * All participants will also receive cisplatin at 60 mg/m\^2 IV on day 2, and etoposide at 80 mg/m\^2 IV daily x3 on days 2 - 4.