A Ph Ib Study of REGN5678 Plus Cemiplimab in Patients With mCRPC

Inclusion Criteria: 1. Men .18 years of age. 2. Histologically or cytologically confirmed adenocarcinoma of the prostate without pure small cell carcinoma. 3. mCRPC with disease progression after at least two lines of systemic therapy, including one line of second-generation anti-androgen therapy, according to one of the following criteria: 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 RECIST Version 1.1 criteria with PCWG3 modifications 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: Prior approved PSMA-targeted therapies \[e.g. 177Lu-PSMA-617\] and immunotherapy (including sipuleucel-T and immune checkpoint therapies) are permitted. 4. Have had either orchiectomy OR be on luteinizing hormone-releasing hormone (LHRH) agonist or antagonist therapy with serum testosterone \<50 ng/dL AND agree to stay on LHRH agonist or antagonist therapy during the study. 5. ECOG performance status (PS) grade of 0 or 1. 6. Adequate organ and bone marrow function documented by: 1. Hemoglobin .8.5 g/dL 2. Absolute neutrophil count .1.0 x 109/L 3. Platelet count .100 x 109/L 7. Serum creatinine .1.5 x ULN or estimated glomerular filtration rate \>50 mL/min/1.73 m2. 8. Adequate hepatic function: 1. Total bilirubin .1.5 x ULN 2. AST .2.5 x ULN 3. ALT .2.5 x ULN 4. Alkaline Phosphatase (ALP) .2.5 x ULN (.5 x ULN if tumor liver or bone involvement). NOTES: Patients with Gilbert fs syndrome do not need to meet total bilirubin requirements provided their total bilirubin is not greater than their historical level. Gilbert fs syndrome must be documented appropriately as past medical history. 9. Consent to MD Anderson laboratory protocols PA13-0291 and Lab02-152. 10. Willing and able to comply with clinic visits and study-related procedures including provision of tumor tissue. 11. Provide informed consent signed by study patient. 12. To avoid risk of drug exposure through the ejaculate (even men with vasectomies), subjects must use a condom during sexual activity while on study drug and for 6 months following the last dose of study drug. If the subject is engaged in sexual activity with a woman of childbearing potential, a condom is required along with another effective contraceptive method consistent with local regulations regarding the use of birth control methods for subjects participating in clinical studies and their partners. Donation of sperm is not allowed while on study drug and for 6 months following the last dose of study drug. Exclusion Criteria: 1. Currently receiving treatment in another interventional study 2. Has participated in a study of an investigational drug within 4-weeks of first dose of study therapy. 3. 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 except for laboratory changes as described in inclusion criteria or patients with grade 2\< neuropathy. 4. Has received radiation therapy or major surgery within 14 days of first administration of study drug or has not recovered (ie, grade .1 or baseline) from AEs, except for laboratory changes as described in inclusion criteria or patients with grade .2 neuropathy. 5. Has received any previous systemic biologic therapy within 5 half-lives of first dose of study therapy. NOTE: Prior treatment with sipuleucel-T is permitted 6. Patients who have not recovered (ie, grade .1 or baseline) from immune-mediated AEs 3 months prior to initiation of study drug therapy except for endocrinopathies adequately managed with hormone replacement. 7. Another malignancy that is progressing or requires active treatment, except: 1. Non-melanoma skin cancer that has undergone potentially curative therapy 2. Any tumor that has been deemed to be effectively treated with definitive local control (with or without continued adjuvant hormonal therapy) 8. Concurrent treatment with systemic corticosteroids (prednisone dose \>10 mg per day or equivalent) or other immunosuppressive drugs \<14 days prior to treatment initiation. Steroids that are topical, inhaled, nasal (spray), or ophthalmic solution are permitted. 9. History of or known or suspected autoimmune disease (exception(s): subjects with vitiligo, resolved childhood atopic dermatitis, hypothyroidism, or hyperthyroidism that is clinically euthyroid at screening are allowed). 10. Known evidence of an active infection requiring systemic therapy such as human immunodeficiency virus (HIV), active hepatitis, or fungal infection. Testing for hepatitis B and C infection will be performed at screening if not previously performed and documented. 11. History of clinically significant cardiovascular disease including, but not limited to: * Myocardial infarction or unstable angina .6 months prior to treatment initiation * Clinically significant cardiac arrhythmia * Deep vein thrombosis, pulmonary embolism, stroke .6 months prior to treatment initiation * Congestive heart failure (New York Heart Association class III-IV) * Pericarditis/clinically significant pericardial effusion * Myocarditis 12. Other prior malignancy (exceptions: adequately treated basal cell or squamous cell skin cancer, superficial bladder cancer, or any other cancer in situ currently in complete remission) .2 years prior to enrollment. 13. 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. 14. Known history of, or any evidence of interstitial lung disease, or active, non-infectious pneumonitis (past 5 years). 15. Receipt of a live vaccine within 4 weeks of planned start of study medication. 16. Prior allogeneic stem cell transplantation or recipients of organ transplants at any time, or autologous stem cell transplantation within 12 weeks of the start of study treatment. 17. Any medical, psychological or social condition that in the opinion of the investigator, would preclude participation in this study.