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The purpose of this study is to assess the safety and efficacy of pembrolizumab (MK-3475) combination therapy in participants with metastatic castration resistant prostate cancer (mCRPC). There will be ten cohorts in this study: Cohort A will receive pembrolizumab + olaparib, Cohort B will receive pembrolizumab + docetaxel + prednisone, Cohort C will receive pembrolizumab + enzalutamide, Cohort D will receive pembrolizumab + abiraterone + prednisone Cohort E will receive pembrolizumab+lenvatinib, Cohort F will receive pembrolizumab+lenvatinib, Cohort G will receive pembrolizumab/vibostolimab coformulation (MK-7684A), Cohort H will receive pembrolizumab/vibostolimab coformulation, Cohort I will receive pembrolizumab+carboplatin+etoposide in Arm 1 and carboplatin+etoposide in Arm 2 and Cohort J will receive belzutifan in Arm1 and Pembrolizumab+belzutifan in Arm 2. Outcome measures will be assessed individually for each cohort.

Assignment of patients to a cohort will be based on prior treatment as outlined in the eligibility criteria. Participants who discontinue pembrolizumab or vibostolimab+pembrolizumab after 35 infusions for reasons other than disease progression or intolerability, or who discontinue pembrolizumab or coformulation of pembrolizumab/vibostolimab after attaining a complete response (and had at least 8 administrations of pembrolizumab or pembrolizumab/vibostolimab coformulation and at least 2 treatments with pembrolizumab or pembrolizumab/vibostolimab coformulation beyond initial complete response) may be eligible to receive a second course of treatment that includes up to 17 additional infusions (approximately 1 year) of pembrolizumab monotherapy or pembrolizumab/vibostolimab coformulation after they have experienced radiographic disease progression after stopping first course treatment. Effective with Protocol Amendment 08, enrollment into Cohorts A, B, C, and D was closed. Effective with Protocol Amendment 14, enrollment into Cohorts E, F, G, and H was closed (not due to any safety issues). No further efficacy and survival follow-up assessments will be collected in Cohorts A through H.