Pembrolizumab-based Therapy in Previously Treated High Grade Neuroendocrine Carcinomas

PRIMARY OBJECTIVE: 1\. Evaluate the best overall response rate (ORR) of pembrolizumab or pembrolizumab plus chemotherapy according to Response Evaluation Criteria in Solid Tumors (RECIST) version 1.1 (investigator-reported). SECONDARY OBJECTIVE: 1. To determine the safety and tolerability of pembrolizumab-based therapy in this patient population. 2. To evaluate duration of response (DOR) in participants receiving pembrolizumab or pembrolizumab plus chemotherapy. 3. To evaluate progression free survival (PFS) in participants treated with pembrolizumab or pembrolizumab plus chemotherapy (median PFS and 18 wk PFS). 4. To evaluate overall survival (OS) in participants receiving pembrolizumab or pembrolizumab plus chemotherapy. OUTLINE: Part A: Participants are treated with pembrolizumab alone. An adaptive Simon's two-stage design was used, and the overall plan hinges on the activity of single agent pembrolizumab in the first stage of Part A. If there is sufficient activity in the first stage of Part A, the study will expand to the second stage of Part A and forgo Part B. If there is insufficient activity in the first stage of Part A, the study will proceed to the first stage of Part B (pembrolizumab plus chemotherapy). Part B: Participants are treated with pembrolizumab plus chemotherapy (physician's choice, paclitaxel or irinotecan). Patients with stable disease (SD) or better after 9 cycles (27 weeks) of pembrolizumab-based therapy will have the option to continue with pembrolizumab alone, unless the first partial response (PR) or complete response (CR) is noted at 27 weeks. All participants will undergo a pre-treatment tumor biopsy (unless the tumor is inaccessible and/or a biopsy is not felt to be in the participant's best interest). Participants may continue study treatment until progressive disease (PD), unacceptable adverse events, inter-current illness that prevents further administration of treatment, investigator's decision to withdraw the participant, the participant withdraws consent, pregnancy of the participant, noncompliance with trial treatment or procedure requirements, participant receives 35 treatments (approximately 2 years) of pembrolizumab, or administrative reasons requiring cessation of treatment.