Study of Opevesostat (MK-5684) Versus Alternative NHA in mCRPC (MK-5684-003)

Inclusion Criteria: * Has histologically- or cytologically-confirmed adenocarcinoma of the prostate without small cell histology. * Has prostate cancer progression while on androgen deprivation therapy (or post bilateral orchiectomy) within 6 months before Screening * Has current evidence of distant metastatic disease (M1 disease) documented by either bone lesions on bone scan and/or soft tissue disease by computed tomography/magnetic resonance imaging (CT/MRI). * Has disease that progressed during or after treatment with 1 novel hormonal agent (NHA) * Has received 1 but no more than 2 taxane-based chemotherapy regimens for metastatic castration-resistant prostate cancer (mCRPC) and has had progressive disease (PD) during or after treatment * Has ongoing androgen deprivation with serum testosterone \<50 ng/dL (\<1.7 nM) * Has provided tumor tissue from a fresh core or excisional biopsy from soft tissue not previously irradiated * Has an Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 assessed within 7 days of randomization * Has had prior treatment with PARPi or were deemed ineligible to receive treatment by the investigator or have refused PARPi treatment * Has received prior 177Lu-PSMA-617 or were deemed ineligible to receive 177Lu-PSMA-617 treatment by the investigator or refused 177Lu-PSMA-617 treatment * Participants who have not received cabazitaxel can be enrolled if they are ineligible for cabazitaxel treatment as determined by the investigator or have refused treatment * If participant received first generation anti-androgen therapy before screening, the participant has evidence of disease progression \>4 weeks since the last flutamide treatment and \>6 weeks since the last bicalutamide or nilutamide treatment * Participants receiving bone resorptive therapy (including, but not limited to, bisphosphonate or denosumab) must have been on stable doses for ≥ 4 weeks before the date of randomization * Participants with human immunodeficiency virus (HIV) infection must have well controlled HIV on antiretroviral therapy (ART) * 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 before randomization * Participants with history of hepatitis C virus (HCV) infection are eligible if HCV viral load is undetectable at Screening. * Participants who can produce sperm must agree to the following during the study treatment period and for at least 7 days after the last dose of opevesostat, for at least 30 days after the last dose of abiraterone acetate, and for at least 3 months after the last dose of enzalutamide: EITHER be abstinent OR must agree to use male condom Exclusion Criteria: * Has a gastrointestinal disorder that might affect absorption * Has a history of pituitary dysfunction * Has poorly controlled diabetes mellitus * Has clinically significant abnormal serum potassium or sodium level * Has a history of active or unstable cardio/cerebro-vascular disease, including thromboembolic events * Has a history of seizure within 6 months of providing documented informed consent or any condition that may predispose to seizures within 12 months before the date of randomization * Has a history of clinically significant ventricular arrhythmias * Has received an anticancer monoclonal antibody (mAb) within 4 weeks before the date of randomization, or has not recovered from adverse events (AEs) due to mAbs administered more than 4 weeks before the date of randomization * Has undergone major surgery, including local prostate intervention (except prostate biopsy), within 28 days before the date of randomization, and has not recovered from the toxicities and/or complications * Participants who have not adequately recovered from major surgery or have ongoing surgical complications * Has used herbal or medicinal products that may have hormonal anti-prostate cancer activity and/or are known to decrease prostate-specific Antigen (PSA) (eg, saw palmetto, megesterol acetate, citrus pectin polysaccharide) within 4 weeks before the date of randomization * Has received radium-223 or lutetium-177 within 4 weeks before the date of randomization, or has not recovered to Grade ≤1 or baseline from AEs due to radium-223 or lutetium-177 administered more than 4 weeks before the date of randomization * Has received treatment with 5-αreductase inhibitors (eg, finasteride or dutasteride), estrogens, or cyproterone within 4 weeks before the date of randomization * Has received colony-stimulating factors within 28 days before the date of randomization * Has received a whole blood transfusion in the last 120 days before the date of randomization. Packed red blood cells and platelet transfusions are acceptable if not given within 28 days of the date of randomization * Has received prior targeted small molecule therapy or NHA treatment within 4 weeks before the first dose of study intervention as follows: enzalutamide or apalutamide within 3 weeks or abiraterone acetate + prednisone or darolutamide within 2 weeks * Has a "superscan" bone scan * Has a diagnosis of immunodeficiency or is receiving chronic systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior the first dose of study medication * Has a known additional malignancy that is progressing or has required active treatment within the past 3 years * Has known active central nervous system (CNS) metastases and/or carcinomatous meningitis * Has an active autoimmune disease that has required systemic treatment in past 2 years * Has an active infection requiring systemic therapy * Has concurrent active HBV or known active HCV infection * Has a history of long QTc syndrome * Has any of the following at Screening Visit: hypotension (systolic BP \<110 mm Hg) or uncontrolled hypertension (systolic BP ≥160 mm Hg or diastolic BP ≥90 mm Hg, in 2 out of 3 recordings with optimized antihypertensive therapy) * Is unable to swallow capsules/tablets * Is currently being treated with cytochrome 450-inducing antiepileptic drugs for seizures * Participants on an unstable dose of thyroid hormone therapy within 6 months before the start of the study intervention * Received prior systemic anticancer therapy including investigational agents within 4 weeks before the first dose of study intervention * 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 dose of study intervention * Systemic use of the following medications within 2 weeks before the first dose of study intervention: strong CYP3A4 inducers (eg, avasimibe, carbamazepine, lumacaftor, phenobarbital, rifampicin, rifapentine, or St John's Wort); P-gp inhibitors (eg, erythromycin, clarithromycin, rifampicin, ketoconazole, itraconazole, posaconazole, artesunate-pyronaridine, ritonavir, indinavir, nelfinavir, atazanavir, glecaprevir-pibrentasvir, simeprevir, ledipasvir-sofosbuvir, verapamil, diltiazem, dronedarone, propafenone, quinidine, cyclosporine, valspodar, or milk thistle \[Silybum marianum\]) * Use of aldosterone antagonist (eg, spironolactone, eplerenone) and phenytoin within 4 weeks before the start of the study intervention