Study of Pembrolizumab (MK-3475) Combination Therapies in Metastatic Castration-Resistant Prostate Cancer (MK-3475-365/KEYNOTE-365)

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.

Inclusion Criteria: * For Cohorts A, B, C, D, E, G, J: Has histologically- or cytologically-confirmed adenocarcinoma of the prostate without small cell histology * For Cohorts F, H, I: Has t-NE or de novo metastatic prostate cancer defined by ≥1% neuroendocrine cells that are located in discrete regions of a recent biopsy specimen from a metastasis as determined by the investigational site and confirmed by central histology review prior to enrollment. Epstein criteria of neuroendocrine differentiation in prostate cancer is used for eligibility. Specimens must have one of the morphologies of Small cell carcinoma or Large cell neuroendocrine carcinoma (LCNEC) or Mixed (small or large cell) NE carcinoma - acinar adenocarcinoma with positive IHC confirmed by central pathology review * Is able to provide tumor tissue from a site not previously irradiated as follows: Cohorts A, E, G and J: must provide a core or excisional biopsy from soft tissue or bone biopsy within 1 year of screening and after developing mCRPC; Cohort B: must provide an archival tumor tissue sample or tumor tissue from a newly obtained core or excisional biopsy from soft tissue if the lesion is clinically accessible; Cohorts C and D with soft tissue disease: must provide a core or excisional biopsy from a soft tissue lesion if clinically accessible within 1 year of screening and after developing mCRPC and an archival specimen if available; and Cohorts F, H, and I must provide a core or excisional biopsy from soft tissue or a bone biopsy. For de novo metastatic neuroendocrine prostate participants, biopsies must be performed within 1 year of screening. Participants with bone metastasis only must provide an archival tumor tissue specimen * Has prostate cancer progression within 6 months prior to screening, as determined by the investigator, by means of one of the following: PSA progression as defined by a minimum of 2 rising PSA levels with an interval of ≥1 week between each assessment where the PSA value at screening should be ≥2 ng/mL; radiographic disease progression in soft tissue based on Response Evaluation Criteria In Solid Tumors Version 1.1 criteria with or without PSA progression; radiographic disease progression in bone defined as the appearance of 2 or more new bone lesions on bone scan with or without PSA progression. Participants with de novo neuroendocrine prostate cancer will not need to provide evidence of progression within 6 months * Has ongoing androgen deprivation with serum testosterone \105 mmHg) at the screening visit * For Cohort C: Has received treatment with 5-α reductase inhibitors (e.g., finasteride, dutasteride), estrogens, and/or cyproterone within 4 weeks prior to Cycle 1 * For Cohort C: Has a history of prostate cancer progression on ketoconazole * For Cohort D: Has received prior treatment with docetaxel or another chemotherapy agent for metastatic prostate cancer * For Cohort D: Has progressed on prior abiraterone acetate for treatment of castration sensitive or resistant metastatic prostate cancer * For Cohort D: Has discontinued prior treatment with abiraterone acetate due to AEs * For Cohort D: Has previously been treated with ketoconazole for prostate cancer for \>7 days * For Cohort D: Has received prior systemic treatment with an azole drug (eg, fluconazole, itraconazole) within 4 weeks of Cycle 1, Day 1 * For Cohort D: Has uncontrolled hypertension (systolic BP ≥ 160 mm Hg or diastolic BP ≥ 95 mm Hg) * For Cohort D: Has a history of pituitary or adrenal dysfunction * For Cohort D: Has clinically significant heart disease as evidenced by myocardial infarction, or arterial thrombotic events in the past 6 months, severe or unstable angina, or New York Heart Association Class II-IV heart disease or cardiac ejection fraction measurement of \480 milliseconds * For Cohorts E and F: Has had major surgery within 3 weeks prior to first dose of study interventions * For Cohorts E and F: Has pre-existing ≥Grade 3 gastrointestinal or non-gastrointestinal fistula * For Cohorts E and F: Has had significant cardiovascular impairment within 12 months of the first dose of study intervention, such as history of New York Heart Association \>Class II congestive heart failure, unstable angina, myocardial infarction, or cerebrovascular accident (CVA)/stroke, cardiac revascularization procedure, or cardiac arrhythmia associated with hemodynamic instability * For Cohorts E and F: Has active hemoptysis (bright red blood of at least 0.5 teaspoon) within 3 weeks prior to the first dose of lenvatinib * For Cohorts E and F: Has gastrointestinal malabsorption or any other condition that might affect the absorption of lenvatinib * For Cohorts G, H, and I: Has had a severe hypersensitivity reaction to treatment with another monoclonal antibody * For Cohorts G, H, and I: Has symptomatic ascites or pleural effusion * For Cohort I: Has clinically active diverticulitis, intra-abdominal abscess, gastrointestinal obstruction, and/or abdominal carcinomatosis * For Cohort I: Has received previous treatment for prostate cancer with platinum-containing compounds