Tremelimumab + Durvalumab(MEDI4736)+ Belinostat in Urothelial Carcinoma

Inclusion Criteria: * Male or female subject aged \>= 18 years * Histologically confirmed urothelial carcinoma with metastatic disease or with unresectable, locally advanced disease. Variant histology, including, but not limited to, neuroendocrine, sarcomatoid, and squamous differentiation are permitted to enroll * Patients must meet one or more of the following criteria: * Has progressed on at least one prior therapy; or * Has declined standard therapy; or * Is not a suitable candidate for standard therapy * The discussion regarding the choice of standard therapy offered, if available, and patient's choice and reason(s) to decline standard therapy should be documented clearly in the research chart. * Patients may have progressed on immune checkpoint inhibitor therapy * Body weight \> 30 kg * Subject must have measurable disease by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 criteria by computed tomography (CT) or magnetic resonance imaging (MRI) * Eastern Cooperative Oncology Group (ECOG) performance status =\< 1 * Absolute neutrophil count (ANC) \>= 1500/mm\^3 * Platelet count \>= 100,000/mm\^3 * Hemoglobin \>= 10 g/dL Hemoglobin \< 10 g/dL due to hematuria at the time of treatment is acceptable as long as there is evidence of adequate bone marrow function in the opinion of the investigator. * Total Bilirubin =\< 1.5 x institutional upper limit of normal (ULN) * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/ala…