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

Key Inclusion 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 and that has progressed within 6 months prior to screening, according to at least 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) Key Exclusion Criteria: 1. Has received treatment with an approved systemic biologic therapy within 3 weeks of dosing or has not yet recovered (ie, grade ≤1 or baseline) from any acute toxicities except for laboratory changes as described in inclusion criteria 2. Has received any previous systemic biologic or anti-cancer immunotherapy within 5 half-lives of first dose of study therapy, as described in the protocol 3. Has received prior Prostate-Specific Membrane Antigen (PSMA)-targeting therapy NOTE: Prior therapy with PSMA-targeting radioligand(s) (eg, 177Lu-PSMA-617) is permitted. However, a period of 12 weeks must elapse between the last dose of the PSMA- targeting radioligand and the first dose of study drug 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 Virus (HBV), or Hepatitis C Virus (HCV) infection; or diagnosis of immunodeficiency, as described in the protocol. NOTE: Other protocol defined Inclusion/Exclusion Criteria apply