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.

Eligibility Criteria:
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