A Clinical Study of Ifinatamab Deruxtecan Based Treatment Combinations or as Monotherapy to Treat Metastatic Castrate Resistant Prostate Cancer (mCRPC) (MK-2400-01A/IDeate-Prostate02)

The purpose of this substudy is to assess the efficacy and safety of ifinatamab deruxtecan (I-DXd), given alone or with other treatments in participants with metastatic castration-resistant prostate cancer (mCRPC). The goals of this study are to learn about: * The safety of the study treatment and if people tolerate it. * A safe dose level of I-DXd that can be used with other treatments. * Participant levels of prostate specific antigen (PSA) during treatment.

This sub study MK-2400-01A assesses treatments for metastatic castration-resistant prostate cancer (mCRPC). The master screening protocol is MK-2400-U01

Inclusion Criteria: The main inclusion criteria include but are not limited to the following: * Has histologically- or cytologically-confirmed adenocarcinoma of the prostate without small cell histology * Has prostate cancer progression while on androgen deprivation therapy (ADT) (or post bilateral orchiectomy) within 6 months before Screening * Has current evidence of metastatic disease * Has received prior treatment with 1 or 2 androgen receptor pathway inhibitors (ARPIs) and progressed during or after treatment * Participants receiving bone resorptive therapy (including, but not limited to bisphosphonate or denosumab) must have been on stable doses for ≥4 weeks before allocation/randomization * An Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1 assessed within 10 days before allocation/randomization * Has prior treatment with poly-ADP-ribose polymerase inhibitors (PARPi) if indicated by local approved regimen or were deemed ineligible to receive PARPi by the investigator Exclusion Criteria: The main exclusion criteria include but are not limited to the following: * History of (non-infectious) interstitial lung disease (ILD)/pneumonitis that required steroids, or has current ILD/pneumonitis or suspected ILD/pneumonitis * Clinically severe pulmonary compromise resulting from intercurrent pulmonary illnesses * Uncontrolled or significant cardiovascular disease * History of pituitary dysfunction * Poorly controlled diabetes mellitus * History or current condition of adrenal insufficiency (eg, Addison's disease) * Has received prior treatment with taxane-based chemotherapy agent for metastatic castration-resistant prostate cancer (mCRPC). * Chronic steroid treatment (dose of \>10 mg daily prednisone equivalent), except for low-dose inhaled steroids (for asthma/chronic obstructive pulmonary disease), topical steroids (for mild skin conditions), or intra-articular steroid injections * Received prior radiotherapy within 2 weeks of start of study intervention, or has radiation-related toxicities, requiring corticosteroids * 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 * History of allogeneic tissue/solid organ transplant