This study is researching an investigational drug called REGN4336 both alone or together with another investigational drug called REGN5678. The study is focused on participants with previously treated metastatic prostate cancer.

The main purpose of the study is to look at the safety, tolerability (how the body reacts to the drug) and effectiveness (how well the drug works to shrink tumors) of REGN4336 when given in combination with REGN5678.

The study has 2 parts. The purpose of Part 1 is to determine a safe dose(s) of REGN4336 to be given alone or in combination with REGN5678. Part 1 is known as the "dose escalation" phase.

The purpose of Part 2, (known as the "dose expansion" phase), is to use the doses of REGN4336 and REGN5678 selected in Part 1 to further test how well the combination treatment with REGN4336 and REGN5678 works to shrink tumors.

The study is looking at several other research questions, including:

• What side effects may happen from taking REGN4336 alone or in combination with REGN5678
• How well does REGN4336 in combination with REGN5678 reduce tumor size
• How much REGN4336 is in the blood at different times when it is given alone or in combination with REGN5678
• Does the body make antibodies against the study drugs (REGN4336 or REGN5678)

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

All Individual Patient Data (IPD) that underlie publicly available results will be considered for sharing

When Regeneron has:

• received marketing authorization from major health authorities (e.g., FDA, European Medicines Agency (EMA), Pharmaceuticals and Medical Devices Agency (PMDA), etc.) for the product and indication or has globally discontinued development of the product for all indications on or after April 2020 and has no plans for future development
• made the study results publicly available (e.g., scientific publication, scientific conference, clinical trial registry)
• the legal authority to share the data, and
• ensured the ability to protect participant privacy

Qualified researchers can submit a proposal for access to individual patient or aggregate level data from a Regeneron-sponsored clinical trial through Vivli. Regeneron's Independent Research Request Evaluation Criteria can be found at: https://www.regeneron.com/sites/default/files/Regeneron-External-Data-Sharing-Policy-and-Independent-Research-Request-Evaluation-Criteria.pdf