MK-5684-01A Substudy: A Phase 1/2 Umbrella Substudy of MK-5684-U01 Master Protocol to Evaluate the Safety and Efficacy of MK-5684-based Treatment Combinations or MK-5684 Alone in Participants With Metastatic Castration-resistant Prostate Cancer (mCRPC)

Inclusion Criteria: The main inclusion criteria include but are not limited to the following: * Histologically or cytologically confirmed diagnosis of adenocarcinoma of the prostate without small cell histology. * Prostate cancer progression and received androgen deprivation therapy (ADT) or post bilateral orchiectomy within 6 months before screening. * Evidence of disease progression from either, \>4 weeks from last flutamide treatment, or \>6 weeks from last bicalutamide or nilutamide treatment, if receiving first generation anti-androgen therapy as last treatment therapy. * Current evidence of metastatic disease. * Prior treatment with 1 to 2 novel hormonal agent(s) (NHA) for non-metastatic, or metastatic, hormone-sensitive prostate cancer or castration-resistant prostate cancer and have disease progression during or after treatment. * Treatment with bone resorptive therapy (including, but not limited to, bisphosphonate or denosumab) must have been on stable doses for \>4 weeks before randomization. * Participants who experienced adverse events (AEs) due to previous anticancer therapies must have recovered to \<Grade 1 or baseline. * Human immunodeficiency virus (HIV)-infected participants must have well controlled HIV on antiretroviral therapy. * Participants who are Hepatitis B surface antigen (HBsAg) positive are eligible if they have received Hepatitis B Virus (HBV) antiviral therapy for at least 4 weeks, and have undetectable HBV viral load. * Participants with a history of Hepatitis C virus (HCV) infection are eligible if HCV viral load is undetectable. Exclusion Criteria: The main exclusion criteria include but are not limited to the following: * History of pituitary dysfunction. * Poorly controlled diabetes mellitus. * Active or unstable cardio/cerebro-vascular disease, including thromboembolic events and history of stroke or transient ischemic attack within 6 months before the first dose of study intervention, history of myocardial infarction within 6 months before the first dose of study intervention, New York Heart Association Class III or IV cardiac disease or congestive heart failure, coronary heart disease that is symptomatic, or unstable angina * History or family history of long corrected QT interval (QTc) syndrome. * Myelodysplastic syndrome (MDS)/acute myeloid leukemia (AML) or features suggestive of MDS/AML. * History or current condition of adrenal insufficiency. * History of (noninfectious) pneumonitis requiring steroids, or current pneumonitis. * HIV-infected participants with a history of Kaposi's sarcoma and/or Multicentric Castleman's Disease. * Undergone major surgery, including local prostate intervention (except prostate biopsy) within 28 days before randomization, and has not recovered from the toxicities and/or complications. * Is on an unstable dose of thyroid hormone therapy within 6 months prior to first dose of study intervention. * Received a whole blood transfusion in the last 120 days before randomization (packed red blood cells and platelet transfusions are acceptable if not given within 28 days before randomization). * Received prior systemic anticancer therapy including investigational agents within 4 weeks before randomization. * Received prior radiotherapy within 2 weeks of start of study intervention or radiation-related toxicities, requiring corticosteroids. * Received a live or live-attenuated vaccine within 30 days before the first does of study intervention. Administration of killed vaccines is allowed. * Diagnosis of immunodeficiency, or is receiving chronic systemic steroid therapy, or any other form of immunosuppressive therapy, within 7 days prior to the first dose of study intervention. * Known additional malignancy that is progressing or has required active treatment within the past 3 years. * Known active central nervous system (CNS) metastases and/or carcinomatous meningitis. * Active autoimmune disease that has required systemic treatment in the past 2 years. * Active infection requiring systemic therapy. * Concurrent active HBV or HCV infections.