Substudy 01A: Safety and Efficacy of Opevesostat (MK-5684)-Based Treatment Combinations or Opevesostat Alone in Participants With Metastatic Castration-resistant Prostate Cancer (mCRPC) (MK-5684-01A)

Eligibility Criteria

• * 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.
• * History of pituitary dysfunction.
• * Poorly controlled diabetes mellitus.
• * Active or unstable cardio/cerebro-vascular disease, including thromboembolic events.
• * 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 and HCV infections.