A Study of Opevesostat (MK-5684) Versus Alternative Next-generation Hormonal Agent (NHA) in Metastatic Castration-resistant Prostate Cancer (mCRPC) Post One NHA (MK-5684-004)

Inclusion Criteria: The main inclusion criteria include but are not limited to the following: * Have histologically or cytologically confirmed adenocarcinoma of the prostate without small cell histology * Has prostate cancer progression while receiving androgen deprivation therapy (ADT) (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 shown by computed tomography (CT)/magnetic resonance imaging (MRI) * Has disease that progressed during or after treatment with one next-generation hormonal agent (NHA) for hormone sensitive prostate cancer (HSPC) (metastatic hormone-sensitive prostate cancer \[mHSPC\] or non-metastatic hormone-sensitive prostate cancer \[nmHSPC\]), or castration-resistant prostate cancer (CRPC) (metastatic castration-resistant prostate cancer \[mCRPC\] or non-metastatic castration-resistant prostate cancer \[nmCRPC\]), for at least 8 weeks of NHA treatment (at least 14 weeks of NHA treatment for participants with bone progression). Note: Participants may have received abiraterone acetate and docetaxel or darolutamide and docetaxel for HSPC. However, participants must have received no more than 6 cycles of docetaxel and had no radiographic disease progression while receiving docetaxel * Has had prior treatment with poly (ADP-ribose) polymerase inhibitor (PARPi) or were deemed ineligible to receive treatment by the investigator or have refused PARPi treatment * Has ongoing androgen deprivation therapy (ADT) with serum testosterone \<50 ng/dL (\<1.7 nM) * Has an eastern clinical oncology group (ECOG) performance status of 0 or 1 assessed within 10 days before randomization * Has adequate organ function * Has provided tumor tissue from a fresh core or excisional biopsy from soft tissue not previously irradiated. Samples from tumors progressing at a prior site of radiation are allowed * 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 have adverse event (AEs) due to previous anticancer therapies must have recovered to ≤Grade 1 or baseline. Participants with endocrine-related AEs who are adequately treated with hormone replacement or participants who have ≤Grade 2 neuropathy or ≤Grade 2 osteopenia/osteoporosis are eligible * Human immunodeficiency virus (HIV)-infected participants must have well controlled HIV on antiretroviral therapy (ART) Exclusion Criteria: The main exclusion criteria include but are not limited to the following: * Has presence of gastrointestinal condition * Is unable to swallow capsules/tablets * Has history of pituitary dysfunction * Has poorly controlled diabetes mellitus * Has clinically significant abnormal serum potassium or sodium level * Has any of the following at screening visit: Hypotension: systolic blood pressure (BP) \<110 mmHg, or uncontrolled hypertension: systolic BP ≥160mmHg or diastolic blood BP ≥90 mmHg, in 2 out of the 3 recordings with optimized antihypertensive therapy * Has a history of active or unstable cardio/cerebrovascular disease, including thromboembolic events * History or family history of long QTc syndrome * Has a history of seizure(s) within 6 months before providing documented informed consent (IC) or has any condition that may predispose to seizure within 12 months prior to the date of enrollment * Has a history of clinically significant ventricular arrhythmias or Mobitz II second degree or third-degree heart block without a permanent pacemaker in place * Has received a taxane-based chemotherapy for metastatic castration-resistant prostate cancer (mCRPC) * Has not adequately recovered from major surgery or have ongoing surgical complications * Is currently being treated with Cytochrome P450 (CYP450)-inducing antiepileptic drugs for seizures * Participants on an unstable dose of thyroid hormone therapy, as judged by the investigator, within 6 months before the start of the study intervention * Receives prior radiotherapy within 2 weeks before the first dose of study intervention, or radiation-related toxicities, requiring corticosteroids * Receives prior systemic anticancer therapy including investigational agents within 4 weeks before the first dose of study intervention * Has systemic use of strong Cytochrome P450 3A4 (CYP3A4) inducers and P-glycoprotein (P-gp) inhibitors within 2 weeks before the first dose of study intervention * Has received prior targeted small molecule therapy or NHA treatment within 4 weeks before the first dose of study intervention * Received a live or live-attenuated vaccine within 30 days before the first dose of study intervention * Has received an investigational agent or has used an investigational device within 4 weeks prior to study intervention administration * Has known hypersensitivity to the components or excipients in abiraterone acetate, prednisone or prednisolone, enzalutamide, fludrocortisone, dexamethasone, or opevesostat * Has a "superscan" bone scan defined as an intense symmetric activity in the bones and diminished renal parenchymal activity on baseline bone scan such that the presence of additional metastases in the future could not be evaluated * Has known additional malignancy that is progressing or has required active treatment within the past 3 years * Diagnosis of immunodeficiency or is receiving chronic systemic steroid therapy (in dosing exceeding 10 mg daily of prednisone equivalent) or any other form of immunosuppressive therapy within 7 days prior the first dose of study medication * Has known active central nervous system (CNS) metastases and/or carcinomatous meningitis. Participants with previously treated brain metastases may participate provided they are radiologically stable, (ie, without evidence of progression) for at least 4 weeks as confirmed by repeat imaging performed during study screening, are clinically stable and have not required steroid treatment for at least 14 days prior to the first dose of study intervention * Has active autoimmune disease that has required systemic treatment in the past 2 years. Replacement therapy is allowed * Active infection requiring systemic therapy * Has concurrent active Hepatitis B virus and Hepatitis C virus infection