Testing the Addition of Tazemetostat to the Immunotherapy Drug, Pembrolizumab (MK-3475), in Advanced Urothelial Carcinoma

Inclusion Criteria: * Patients must have pathologically confirmed urothelial carcinoma * Note: Patients with mixed histology (with predominant urothelial carcinoma) are eligible * Patients must have locally advanced or metastatic disease with either: * Arm A: Disease progression during or following (within 12 months) platinum-based chemotherapy (cisplatin or carboplatin) * Note: No minimum number of cycles on platinum-based chemotherapy are required. Patients who have had multiple rounds of platinum-based chemotherapy with events of intermittent progressive disease (PD) are eligible as long as progression has been confirmed while on or within 12 months from platinum based therapy OR * Arm B: Platinum ineligible status (i.e., patients unable to receive platinum-containing chemotherapy, in the opinion of the treating investigator, regardless of PD-L1 status) or chemotherapy ineligible status (i.e., patients unable to receive treatment with any chemotherapy, in the opinion of the treating investigator, regardless of PD-L1 status) * Note: The eligible patient population for Arm B was revised in protocol amendment 10 from 'cisplatin ineligible patients with PD-L1 positive disease' to 'platinum ineligible patients (i.e., unable to receive platinum-containing chemotherapy, in the opinion of the treating investigator, regardless of PD-L1 status) or chemotherapy ineligible patients (i.e., unable to receive treatment with any chemotherapy, in the opinion of the treat…