A Trial to Find Out if REGN4336 is Safe and How Well it Works Alone and in Combination With Cemiplimab or REGN5678 for Adult Participants With Advanced Prostate Cancer

Eligibility Criteria

• 1. Histologically or cytologically confirmed adenocarcinoma of the prostate without pure small cell carcinoma
• 2. Metastatic, castration-resistant prostate cancer (mCRPC) with PSA value at screening ≥4 ng/mL that has progressed within 6 months prior to screening, according to 1 of the following:
• 1. PSA progression as defined by a rising PSA level confirmed with an interval of ≥1 week between each assessment
• 2. Radiographic disease progression in soft tissue based on Response Evaluation Criteria in Solid Tumors (RECIST) version 1.1 criteria with or without PSA progression
• 3. Radiographic disease progression in bone defined as the appearance of 2 or more new bone lesions on bone scan with or without PSA progression NOTE: Measurable disease per RECIST version 1.1 per local reading at screening is not an eligibility criterion for enrollment
• 3. Has progressed upon or intolerant to ≥2 lines prior systemic therapy approved in the metastatic and/or castration-resistant setting (in addition to androgen deprivation therapy \[ADT\]) including at least one second-generation anti-androgen therapy (e.g. abiraterone, enzalutamide, apalutamide, or darolutamide)
• 1. Has received treatment with an approved systemic therapy within 3 weeks of dosing or has not yet recovered (ie, grade ≤1 or baseline) from any acute toxicities
• 2. Has received any previous systemic biologic or immune-modulating therapy (except for Sipuleucel-T) within 5 half-lives of first dose of study therapy, as described in the protocol
• 3. Has received prior PSMA-targeting therapy. Exception: Prior therapy with approved PSMA-targeted radioligand(s) is permitted
• 4. Any condition that requires ongoing/continuous corticosteroid therapy (\>10 mg prednisone/day or anti-inflammatory equivalent) within 1 week prior to the first dose of study therapy
• 5. Ongoing or recent (within 5 years) evidence of significant autoimmune disease that required treatment with systemic immunosuppressive treatments
• 6. Encephalitis, meningitis, neurodegenerative disease (with the exception of mild dementia that does not interfere with activities of daily living \[ADLs\]) or uncontrolled seizures in the year prior to first dose of study therapy
• 7. Uncontrolled infection with human immunodeficiency virus (HIV), hepatitis B or hepatitis C infection; or diagnosis of immunodeficiency, as described in the protocol.