The purpose of this study is to evaluate the safety, efficacy, tolerability, and pharmacokinetics (PK) of FG-3246, a cluster of differentiation 46 (CD46) targeting antibody-drug conjugate (ADC), in the treatment of participants with mCRPC who have progressed following treatment with one prior second-generation androgen receptor signaling inhibitor (ARSI) in any setting and no prior taxane therapy in the mCRPC setting.

Key Inclusion Criteria:

• Participant must have histological, and/or cytological confirmation of prostate adenocarcinoma on all prior tumor biopsies.
• Participant with soft tissue disease and a safely accessible soft tissue tumor lesion(s) must agree to biopsy of a primary or metastatic lesion during screening. Alternatively, participant may provide a suitable archival biopsy of a primary or metastatic lesion.
• Participant must have serum testosterone levels <50 nanograms (ng)/deciliter (dL) during screening.
• Participant is required to have progressed on no more than one prior treatment with a second generation ARSI (abiraterone acetate, enzalutamide, apalutamide, or darolutamide) initiated in either the castration-sensitive or castration-resistant setting.
• Participant must have progressive mCRPC following last treatment at screening.
• Participant must have ≥1 metastatic lesion that is present on baseline Computed Tomography (CT), Magnetic Resonance Imaging (MRI), or bone scan obtained ≤28 days prior to randomization.
• Participant must have adequate organ function during screening.

Key Exclusion Criteria:

• Participant has received previous treatment with a therapeutic targeting CD46.
• Participant has small cell neuroendocrine carcinoma (pure or mixed) on any prior histologic evaluation of primary or metastatic lesion.
• Participant has progressed on more than one prior second-generation ARSI in any setting or has received more than two prior second-generation ARSIs in any setting.
• Participants must not have received recent anticancer treatments before enrollment. Ongoing supportive or hormonal therapies are allowed if they were started well before randomization and are continued without change.
• Participant has received any prior radiation therapy within 14 days prior to randomization.
• Participant has a known actionable mutation or gene alteration, for example, BRCA1 mutation, for which approved therapies are available, for example, PARP inhibitors, unless these therapies are not appropriate for the participant as determined by the investigator or the participant refuses such therapy.
• Participant has National Cancer institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE) ≥Grade 2 peripheral neuropathy at the time of screening from any etiology.
• Participant has received any prior chemotherapy; however, one prior taxane-based chemotherapy in the castration-sensitive setting is allowed if completed >12 months before randomization.
• Participant has known hypersensitivity to the components of FG-3246 or its analogs or a history of allergic or anaphylactic reaction to human, humanized, or chimeric monoclonal antibodies.
• Participant has diagnosis with any other malignancy in the past 5 years, except for adequately treated basal cell or squamous cell carcinoma of the skin.
• Participant requires treatment with a strong cytochrome P450 3A4 (CYP3A4) inhibitor or inducer drug that cannot be safely discontinued.

NOTE: Other protocol-defined inclusion/exclusion may apply.