Apalutamide Plus Cetrelimab in Patients With Treatment-Emergent Small Cell Neuroendocrine Prostate Cancer

Inclusion Criteria: 1. Participants must have histologically confirmed prostate adenocarcinoma at the time of diagnosis, with subsequent development of metastatic castration-resistant prostate cancer. Prostate adenocarcinoma with neuroendocrine features (e.g. positive chromogranin and/or synaptophysin expression by IHC) is allowed. 2. Evidence of disease progression (PD) by PSA and/or radiographic progression by Prostate Cancer Clinical Trials Working Group 3 (PCWG3) criteria at the time of study entry. 3. Prior progression on at least one androgen signaling inhibitor (e.g. abiraterone acetate, apalutamide, enzalutamide, darolutamide ). Treatment with prior androgen signaling inhibitor may have been initiated in either the castration-sensitive prostate cancer (CSPC) and/or CRPC setting. 4. Patients must be evaluable for the primary endpoint of composite response and must have either serum Prostate-specific antigen (PSA) \> 2 ng/mL during screening and/or measurable disease by RECIST 1.1 criteria. 5. Participants must have clinicogenomic evidence of treatment emergent small cell neuroendocrine prostate cancer as defined by one or more of the following: 1. Histologic evidence of small cell neuroendocrine prostate cancer on evaluation of castrate resistant prostate cancer (CRPC) tissue by centralized pathology review and/or 2. Presence of loss-of-function mutation or deletion of Retinoblastoma (RB1) gene on a Clinical Laboratory Improvement Amendments (CLIA)-approved genomic-sequencing platform. Either monoallelic or biallelic mutations in RB1 are allowed. 6. No more than one prior line of taxane-based chemotherapy administered in the metastatic castrate resistant prostate cancer (mCRPC) setting. Chemotherapy administered in the castration-sensitive setting does not count towards this limit. Prior carboplatin is allowed and does not count as an additional line of therapy when given in conjunction with taxane. 7. Castrate level of serum testosterone at study entry (\<50 ng/dL). Patients without prior bilateral orchiectomy are required to remain on Luteinizing hormone-releasing hormone (LHRH) analogue treatment for duration of study. 8. No other systemic anti-cancer therapies administered other than LHRH analogue within 14 days or, 5 half-lives, whichever is shorter, prior to initiation of study treatment. Adverse Events (AEs) related to prior anti-cancer treatment must have recovered to Grade \<= 1 with the exception of any grade alopecia and Grade \<= 2 neuropathy. a. Patients receiving apalutamide prior to study entry may continue treatment at their current apalutamide dose level without requirement for wash-out period. 9. Age \>= 18 years 10. Eastern Cooperative Oncology Group (ECOG) performance status \<= 1 (Karnofsky performance status \>= 70%) 11. Demonstrates adequate organ function as defined below: 1. Absolute neutrophil count \>= 1,500/microliter (mcL) 2. Platelets \>= 100,000/mcL 3. Hemoglobin \>= 9.0 g/dL 4. Total bilirubin \<= 1.5 x institutional upper limit of normal (ULN), unless elevated due to Gilbert's syndrome and direct bilirubin is within normal limits 5. Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase (SGOT)) \<=3 X institutional upper limit of normal (\<= 5 x ULN in presence of liver metastases) 6. Alanine aminotransferase (ALT) (serum glutamic-pyruvic transaminase (SGPT)) \<=3 X institutional upper limit of normal (\<= 5 x ULN in presence of liver metastases) 7. Serum creatinine \<= 1.5 x institutional upper limit of normal 12. Ability to understand a written informed consent document, and the willingness to sign it. 13. Patients must agree to use adequate contraception and to not donate sperm prior to the study, for the duration of study participation, and 5 months after last administration of study treatment. Adequate contraception includes: 1. Patients who are sexually active should consider their female partner to be of childbearing potential if she has experienced menarche and is not postmenopausal (defined as amenorrhea \> 24 consecutive months) or has not undergone successful surgical sterilization. 2. Even participants who have undergone vasectomy should still use acceptable method of contraception. 3. Acceptable methods of contraception include hormonal combined (estrogen + progesterone) or progesterone only given orally, injected or implanted; intrauterine device (IUD), non hormonal intrauterine systems (IUS), tubal ligation, vasectomy and complete sexual abstinence. 14. Patients must be willing to undergo metastatic tumor biopsy during Screening if no biopsy has previously been done. If no metastatic lesion is safely accessible to tumor biopsy, this requirement will be waived. Bone or soft tissue lesion is allowed, but soft tissue will be prioritized. If a patient has archival tissue obtained within 90 days of cycle 1 day 1 (C1D1) the requirement for fresh tumor biopsy will be waived. Exclusion Criteria: 1. De novo small cell carcinoma of the prostate. 2. Has participated in a study of an investigational product and received study treatment or used an investigational device other than those specified in the protocol within 2 weeks of C1D1. 3. Hypersensitivity to cetrelimab, apalutamide, or any of its excipients. 4. Has received prior radiotherapy within 2 weeks of C1D1. Participants must have recovered from all radiation-related toxicities, not require corticosteroids, and not have had radiation pneumonitis. A 1-week washout is permitted for palliative radiation (\<=2 weeks of radiotherapy) to non-central nervous system (CNS) disease. 5. Receipt of prior cetrelimab or another immune checkpoint inhibitor targeting PD-1/PD-L1 and/or cytotoxic T-lymphocyte-associated protein 4 (CTLA-4) (e.g. pembrolizumab, nivolumab, ipilimumab). Prior treatment with sipuleucel-T is allowed. 6. Has an active autoimmune disease that has required systemic treatment in the past 2 years (i.e., with use of disease modifying agents, corticosteroids or immunosuppressive drugs). Patients on low dose oral weekly methotrexate are allowed. Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency) or treatment with drugs (e.g. methimazole, neomercazole, carbimazole, etc.) that function to decrease the generation of thyroid hormone by a hyper-functioning thyroid gland (e.g., in Graves' disease) is not considered a form of systemic treatment of an autoimmune disease. 7. Has received a live vaccine within 30 days prior to the first dose of study drug. Examples of live vaccines include, but are not limited to, the following: measles, mumps, rubella, varicella/zoster (chicken pox), yellow fever, rabies, Bacillus Calmette-Guérin (BCG), and typhoid vaccine. Seasonal influenza vaccines for injection are generally killed virus vaccines and are allowed; however, intranasal influenza vaccines (e.g., FluMist®) are live attenuated vaccines and are not allowed. Coronavirus-2019 (COVID-19) vaccine is allowed. 8. Individuals with concurrent second malignancy requiring active treatment at study entry that could affect safety or efficacy endpoints. Non-melanoma skin cancer, non-muscle invasive bladder cancer, and other carcinomas-in-situ are allowable exceptions. 9. Cardiac condition as defined as one or more of the following: 1. Uncontrolled supraventricular arrhythmia or ventricular arrhythmia requiring treatment 2. New York Heart Association (NYHA) congestive heart failure class III or IV 3. History of unstable angina, myocardial infarction, or cerebrovascular accident within 6 months prior to C1D1 4. Uncontrolled hypertension defined as systolic BP (SBP) \>= 160 mm Hg and/or diastolic BP (DBP) \>= 100 mmHg. Treatment and re-screening are permitted. 10. History of seizure or pre-disposing condition (e.g. brain metastases). Medications known to lower seizure threshold must be discontinued at least 4 weeks prior to C1D1. 11. Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy at a prednisone equivalent dose of \> 10 mg daily or other form of immunosuppressive therapy within 7 days prior to first dose of study drug. 12. Human immunodeficiency virus (HIV)-infected individuals on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial (screening not required in the absence of risk factors). 13. For participants with evidence of chronic hepatitis B virus (HBV) infection (positive hepatitis B surface antigen (HBsAg) and/or hepatitis C antibody (HBcAb)), the HBV viral load must be undetectable at the time of study enrollment (screening not required in the absence of risk factors). 14. Chronic active hepatitis C virus (HCV) infection defined as positive viral load (screening not required in the absence of risk factors). 15. Has a history of (non-infectious) pneumonitis that required steroids or has current pneumonitis. 16. Gastrointestinal disorder affecting absorption. 17. Has an active infection requiring intravenous (IV) antibiotics within 7 days prior to C1D1. 18. Use of a prohibited concomitant medication within 7 days of C1D1. Medications known to lower seizure threshold must be discontinued at least 4 weeks prior to C1D1. 19. Major surgery within 28 days prior to C1D1. Minor procedures including biopsies, dental surgery, cataract surgery, or outpatient procedure are allowed 20. Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the study, interfere with the subject's participation for the full duration of the study, or is not in the best interest of the subject to participate, in the opinion of the treating investigator. 21. Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial.