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)

Substudy 01A is part of a larger research study that is testing experimental treatments for metastatic castration-resistant prostate cancer (mCRPC). The larger study is the umbrella study (U01). The goal of substudy 01A is to evaluate the safety and efficacy of opevesostat-based treatment combinations, or as a single agent, in participants with mCRPC. This substudy will have two phases: a safety lead-in phase and an efficacy phase. The safety lead-in phase will be used to evaluate the safety and tolerability, and to establish a recommended Phase 2 dose (RP2D) for the opevesostat-based treatment combinations. There will be no hypothesis testing in this study.

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 \