A Trial of BXCL701 and Pembrolizumab in Patients With mCRPC Either Small Cell Neuroendocrine Prostate Cancer or Adenocarcinoma Phenotype.

Inclusion Criteria: All patients must satisfy the following inclusion and exclusion criteria to be eligible for entry into the trial. 1. Patient has evidence of progressive, metastatic castration-resistant disease, as defined by PCWG3 criteria. a. Patients with de novo small cell prostate cancer are not required to have received androgen deprivation therapy (ADT). 2. Progression during or following completion of at least 1 prior line of systemic therapy for locally advanced or metastatic prostate cancer. 3. Phases 2a and 2b Only: SCNC - Cohort A of Phase 2a only: 1. Patient has histologic evidence of SCNC either with archival tissue or a fresh tumor biopsy obtained during screening. Tumor biopsy tissue must be submitted for a central laboratory pathology review; however, enrollment can proceed if SCNC is determined by a local pathology review. 2. Patient has previously received at least 1 prior line of cytotoxic chemotherapy. Patients who either have refused chemotherapy or are considered unsuitable for chemotherapy may be eligible following discussion with the sponsor. 3. Must be willing to undergo metastatic tumor biopsy during Screening. Requirement may be waived in patients without safely accessible lesion or for patients with evaluable archival metastatic tumor tissue 4. Has measurable disease per RECIST 1.1 criteria. Adenocarcinoma - Cohort B of Phase 2a; randomized population for Phase 2b 1. Patient has histologically or cytologically confirmed adenocarcinoma of the prostate without small cell neuroendocrine features. 2. Patients with soft tissue disease must provide a fresh core or excisional biopsy or archival tissue from a site not previously irradiated for central pathology review; however enrollment may proceed if predominant adenocarcinoma without small cell neuroendocrine features is determined by local pathology review. 3. Has been treated with at least 1 but no more than 2 second generation AR pathway target agents (e.g., abiraterone acetate and/or enzalutamide or other next generation agent) and at least 1 regimen/line of taxane containing chemotherapy in the mCSPC or mCRPC setting. Patients with known actionable mutations should have progressed on applicable standard care targeted therapy or have documented intolerance to or be unsuitable for such therapy. 4. RECIST 1.1 measurable disease or detectable bone metastases by whole body bone scintigraphy. 4. Patient has serum testosterone \<50 ng/dL during Screening except for those with de novo small cell prostate cancer. a. Patients with treatment-emergent SCNC without a history of bilateral orchiectomy are required to remain on luteinizing hormone-releasing hormone (LHRH) analog during the course of protocol therapy except for patients with de novo small cell prostate cancer. 5. Patient has Eastern Cooperative Oncology Group (ECOG) performance status of 0-2. 6. Patient is ≥18 years of age. 7. Patient's acute toxic effects of previous anticancer therapy have resolved to ≤Grade 1 except for Grade 2-3 peripheral neuropathy or any grade of alopecia. 8. Patient has adequate baseline organ function, as demonstrated by the following: 1. Serum creatinine ≤1.5 times institutional upper limit of normal (ULN) or calculated creatinine clearance \>50 mL/min; 2. Serum albumin ≥2.5 g/dL; 3. Total bilirubin ≤1.5 × ULN; 4. Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤2.5 × institutional ULN (patients with hepatic metastases must have AST/ALT ≤5 × ULN). 9. Patient has adequate baseline hematologic function, as demonstrated by the following: 1. Absolute neutrophil count (ANC) ≥1.5 × 109/L. 2. Hemoglobin ≥8 g/dL and no red blood cell transfusions during the prior 14 days. 3. Platelet count ≥100 × 109/L and no platelet transfusions during the prior 14 days. 10. Male patients and their female partners of childbearing potential must agree and commit to use a barrier contraception throughout the duration of the study until at least 6 months following the last dose of study drug, in addition to their female partners using either an intrauterine device or hormonal contraception and continuing until at least 6 months following the last dose of study drug. This criterion may be waived for male patients who have had a vasectomy \>6 months before signing the informed consent form. Exception: In the United States, female partners of study participants are not required to use contraception as a condition of their partners' eligibility, but female partners with child bearing potential should consider use of effect methods of contraception for the duration of their male partners' study participation and for at least 6 months following the last dose of study medication. 11. Patient has signed informed consent prior to initiation of any study-specific procedures or treatment. 12. Patient is able to adhere to the study visit schedule and other protocol requirements, including follow-up for overall survival (OS). Exclusion Criteria: 1. Patient has received treatment with \>2 cytotoxic chemotherapy regimens for castration-resistant prostate cancer (CRPC). Chemotherapy in the hormone-sensitive setting does not count in this assessment provided the last dose was \>6 months before study entry. A change in chemotherapy agents due to intolerance after brief exposure may not count in this assessment, pending review with Medical Monitor. 2. Patient has received external-beam radiation or another systemic anticancer therapy within 14 days or 5 half-lives, whichever is shorter, prior to study treatment. 3. Patient has received treatment with an investigational systemic anticancer agent within 14 days prior to study drug administration. 4. Patient has received prior treatment with an anti-PD-1, anti-PD-L1, anti-programmed death ligand 2 (PD-L2) agent or with an agent directed to another co-inhibitory T-cell receptor (e.g., cytotoxic T lymphocyte-associated antigen 4 \[CTLA-4\], OX-40, CD137) or requires concomitant treatment with DPP4 inhibitors. 5. Patient has an additional active malignancy that may confound the assessment of the study endpoints. If the patient has a past cancer history (active malignancy within 2 years prior to study entry) with substantial potential for recurrence, this must be discussed with the sponsor before study entry. Patients with the following concomitant neoplastic diagnoses are eligible: non-melanoma skin cancer and carcinomas in situ (including transitional cell carcinoma, anal carcinoma, and melanoma in situ). 6. Patient has clinically significant cardiovascular disease (e.g., uncontrolled or any New York Heart Association Class 3 or 4 congestive heart failure, uncontrolled angina, history of myocardial infarction, unstable angina or stroke within 6 months prior to study entry, uncontrolled hypertension or clinically significant arrhythmias not controlled by medication). 7. QT interval corrected for heart rate using Bazett's formula (QTcB) \>480 msec at Screening. 8. Patient has uncontrolled, clinically significant pulmonary disease (e.g., chronic obstructive pulmonary disease, pulmonary hypertension) that in the opinion of the investigator would put the patient at significant risk for pulmonary complications during the study. 9. Patient has brain or leptomeningeal metastases that are symptomatic and progressive on imaging. Patients with a history of central nervous system (CNS) metastases must have received appropriate treatment. Central nervous system imaging is not required prior to study entry unless there is a history of CNS involvement or clinical suspicion of CNS involvement. Imaging of patients with a prior history of CNS metastases should be compared to prior imaging to discern disease progression. 10. Patient has an active autoimmune disease or Grade ≥3 non-infectious pneumonitis that has required systemic treatment in the past 2 years (i.e., with use of disease modifying agents, corticosteroids, or immunosuppressive drugs). Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency) or treatment with drugs (e.g., neomercazol, carbimazole) that function to decrease the generation of thyroid hormone by a hyperfunctioning thyroid gland (e.g., in Graves' disease) is not considered a form of systemic treatment of an autoimmune disease. 11. Patient has a diagnosis of immunodeficiency or is receiving systemic steroid therapy at a prednisone equivalent dose of \>10 mg daily for at least 1 week or other form of immunosuppressive therapy within 7 days prior to Cycle 1 Day 1 (C1D1). 12. Patient has uncontrolled intercurrent illness including, but not limited to, uncontrolled infection, suspected or active SARS-CoV-2 (COVID-19) infection, disseminated intravascular coagulation, or psychiatric illness/social situations that would limit compliance with study requirements. 13. Patient has known positive status for human immunodeficiency virus, active or chronic Hepatitis B, or Hepatitis C. Screening is not required. 14. Patient has any medical condition which, in the opinion of the investigator, places the patient at an unacceptably high risk for toxicity. 15. Any dysphagia, odynophagia, esophageal dysmotility or stricture, known GI malabsorption syndrome, or intractable diarrhea that may significantly alter the absorption of orally administered study drug. 16. Patients with history of symptomatic orthostatic hypotension within 3 months prior to enrollment. Orthostatic hypotension is defined as a drop in systolic blood pressure (BP) of ≥ 20 mmHg or diastolic BP of ≥ 10 mmHg with assumption of an upright posture.