Phase II Trial of Zanzalitinib in Patients With Metastatic Castration Resistant Prostate Cancer

Inclusion Criteria: * Participants must have histologically or cytologically confirmed metastatic castrate-resistant prostate cancer. Adenocarcinoma of prostate must be primary histology, but neuroendocrine features are allowed as long as \<50% neuroendocrine histology. Tissue is not mandatory, but a pathologic report is required at time of participant enrollment. * Participants must have evidence of metastatic disease in soft tissue or visceral disease on conventional scans including CT and bone scans * Participants must have previously been treated with an ARPI (abiraterone, enzalutamide, apalutamide, darolutamide). Prior exposure to 1 line of taxane-based chemotherapy (docetaxel) is allowed. * Age ≥ 18 years. * Karnofsky Performance status ≥ 60% * Participants must have adequate organ and marrow function, based upon meeting all the following laboratory criteria within 14 days before first dose of study treatment as defined below: * Absolute neutrophil count (ANC) ≥ 1500/mm3 (≥ 1.5 GI/L) without granulocyte colony-stimulating factor support within 2 weeks of screening laboratory sample collection. * Platelets ≥ 100,000/mm3 (≥ 100 GI/L) without transfusion within 2 weeks of screening laboratory sample collection. * Hemoglobin ≥ 9 g/dL (≥ 90 g/L) without transfusion within 2 weeks prior to screening laboratory sample collection. * International Normalized Ratio (INR) ≤ 1.5 and activated partial thromboplastin time (aPTT) ≤ 1.2 x upper limit of normal (ULN). * Alanine aminotransferase (ALT), aspartate aminotransferase (AST), and alkaline phosphatase (ALP) ≤ 3 x ULN. For participants with documented bone metastasis ALP ≤ 5 x ULN. For participants with CRPC and bone metastasis ALP ≤ 10 x ULN if predominantly bone-specific ALP. * Total bilirubin ≤ 1.5 x ULN (for participants with Gilbert's disease ≤ 3 x ULN). * Serum creatinine ≤ 1.5 x ULN or calculated creatinine clearance ≥ 40 mL/min (≥ 0.67 mL/sec) using the Cockcroft Gault equation. * Urine protein-to-creatinine ratio (UPCR) ≤ 1 mg/mg (≤ 113.2 mg/mmol) creatinine. * Recovery to baseline or ≤ Grade 1 severity (CTCAE v5) from adverse events (AEs), including immune-related adverse events (irAEs), related to any prior treatments, unless AE(s) are clinically nonsignificant and/or stable on supportive therapy (eg, physiological replacement of corticosteroid). Low-grade or controlled toxicities such as alopecia, ≤ Grade 2 hypomagnesemia, ≤ Grade 2 neuropathy are permitted) * Participants must be capable of understanding and complying with the protocol requirements and must have signed the informed consent document. * Sexually active fertile participants and their partners must agree to use highly effective method of contraception (defined in Appendix III) during the course of the study and for the following durations after the last dose of treatment (whichever is later). An additional contraceptive method, such as a barrier method (eg, condom), is required. In addition, men must agree not to donate sperm and women must agree not to donate eggs (ova, oocyte) for the purpose of reproduction during these same periods: * through 186 days after the last dose of zanzalintinib for women of childbearing potential (WOCBP) or through 96 days after the last dose of zanzalintinib for men Exclusion Criteria: * Evidence of hormone-sensitive prostate cancer (HSPC). * Evidence of small cell prostate cancer. * Prior treatment with any TKI (including zanzalintinib) * Receipt of any type of small molecule kinase inhibitor (including investigational kinase inhibitor) within 2 weeks before first dose of study treatment. * Receipt of any type of cytotoxic, biologic or other systemic anticancer therapy (including investigational) within 2 weeks before first dose of study treatment. * The antiandrogen abiraterone is permitted up to 1 week prior to first dose of study treatment. Concomitant use of megestrol acetate or leuprolide is permitted. Other types of hormonal therapies with similar use require prior approval from the Principal Investigator. * Another malignancy that requires active therapy and in the opinion of the Investigator would interfere with monitoring of radiologic assessments of response to Investigational Product, within 2 years before first dose of study treatment, except for superficial skin cancers, or localized, low-grade tumors deemed cured and not treated with systemic therapy. * Participants with BRCA-mutated mCRPC who have not previously received a PARP inhibitor * Participants with MSI-H mCRPC who have not previously received pembrolizumab or another immune-checkpoint inhibitor for treatment of MSI-H mCRPC * Radiation therapy for bone metastasis within 2 weeks, any other radiation therapy within 4 weeks before first dose of study treatment. Systemic treatment with radionuclides within 6 weeks before first dose of study treatment. Participants with clinically relevant ongoing complications from prior radiation therapy are not eligible. * Known brain metastases or cranial epidural disease unless adequately treated with radiotherapy and/or surgery (including radiosurgery) and stable for at least 4 weeks before first dose of study treatment. Note: Eligible participants must be neurologically asymptomatic and without corticosteroid treatment at the time of enrollment. * Base of skull lesions without definitive evidence of dural or brain parenchymal involvement are allowed. * Concomitant anticoagulation with oral anticoagulants (eg, warfarin, direct thrombin inhibitors ) and platelet inhibitors (eg, clopidogrel). * Allowed anticoagulants are the following: * Prophylactic use of low-dose aspirin for cardio-protection (per local applicable guidelines) and low-dose low molecular weight heparins (LMWH). * Therapeutic doses of LMWH or anticoagulation with direct factor Xa inhibitors rivaroxaban, edoxaban, or apixaban in participants without known brain metastases who are on a stable dose of the anticoagulant for at least 1 week before first dose of study treatment without clinically significant hemorrhagic complications from the anticoagulation regimen. Note: Participants must have discontinued oral anticoagulants within 3 days or 5 half-lives prior to first dose of study treatment, whichever is longer. * The participant has uncontrolled, significant intercurrent or recent illness including, but not limited to, the following conditions: * Unstable or deteriorating cardiovascular disorders: * Congestive heart failure New York Heart Association Class 3 or 4, class 2 or higher, unstable angina pectoris, new-onset angina, serious cardiac arrhythmias (eg, ventricular flutter, ventricular fibrillation, Torsades de pointes). * Uncontrolled hypertension defined as sustained blood pressure (BP) \> 140 mm Hg systolic or \> 90 mm Hg diastolic despite optimal antihypertensive treatment. * Stroke (including transient ischemic attack \[TIA\]), myocardial infarction, or other clinically significant arterial thrombotic and/or ischemic event within 6 months before first dose of study treatment. * Pulmonary embolism (PE) or deep vein thrombosis (DVT) or prior clinically significant venous events within 3 months before first dose of study treatment. * Note: Participants with a diagnosis of DVT within 6 months are allowed if asymptomatic and stable at screening and are on a stable dose of the anticoagulant for at least 1 week before first dose of study treatment without clinically significant hemorrhagic complications from the anticoagulation regimen. * Note: Participants who don't require prior anticoagulation therapy may be eligible but must be discussed and approved by the Principal Investigator. * Gastrointestinal (GI) disorders including those associated with a high risk of perforation or fistula formation: * Tumors invading the GI-tract from external viscera * Active peptic ulcer disease, inflammatory bowel disease, diverticulitis, cholecystitis, symptomatic cholangitis or appendicitis, or acute pancreatitis * Acute obstruction of the bowel, gastric outlet, or pancreatic or biliary duct within 6 months before first dose unless cause of obstruction is definitively managed and participant is asymptomatic * Abdominal fistula, gastrointestinal perforation, bowel obstruction, or intra-abdominal abscess within 6 months before first dose. Note: Complete healing of an intra-abdominal abscess must be confirmed before first dose of study treatment. * Known gastric or esophageal varices * Ascites, pleural effusion, or pericardial fluid requiring drainage in last 4 weeks * Clinically significant hematuria, hematemesis, or hemoptysis of \> 0.5 teaspoon (2.5 ml) of red blood, or other history of significant bleeding (eg, pulmonary hemorrhage) within 12 weeks before first dose of study treatment. * Symptomatic cavitating pulmonary lesion(s) or endobronchial disease (asymptomatic or radiated lesions allowed) * Lesions invading major blood vessel including, but not limited to, inferior vena cava, pulmonary artery, or aorta. Note: Participants with intravascular tumor extension may be eligible following Principal Investigator approval. * Other clinically significant disorders that would preclude safe study participation: * Active infection requiring systemic treatment. * Note: Prophylactic antimicrobial treatments (antibiotics, antimycotic, antiviral) are allowed. * Known infection with acute or chronic hepatitis B or C, known human immunodeficiency virus (HIV) or acquired immunodeficiency syndrome (AIDS)-related illness except for participants meeting all of the following criteria: (1) on stable anti-retroviral therapy; (2) CD4+ T cell count ≥ 200/µL; and (3) an undetectable viral load. * Note: HIV testing will be performed at screening if and as required by local regulation. * Note: To be eligible, participants taking CYP inhibitors (eg, zidovudine, ritonavir, cobicistat, didanosine) or CYP3 inducers (efavirenz) must change to a different regimen not including these drugs 7 days prior to initiation of study treatment. Anti-retroviral therapies (ART) must have been received for at least 4 weeks prior to the first dose. * Note: CD4+ T cell counts, and viral load are monitored per standard of care by the local health care provider. * Serious non-healing wound/ulcer/bone fracture. * Note: non-healing wounds or ulcers are permitted if due to tumor-associated skin lesions. * Malabsorption syndrome. * Pharmacologically uncompensated, symptomatic hypothyroidism. * Moderate to severe hepatic impairment (Child-Pugh B or C). * Requirement for hemodialysis or peritoneal dialysis. * History of solid organ or allogeneic stem cell transplant. * Major surgery (as defined in Appendix IV; eg, GI surgery, removal or biopsy of brain metastasis) within 8 weeks prior to first dose of study treatment. Prior laparoscopic surgeries (ie nephrectomy) within 4 weeks prior to first dose of study treatment. Minor surgery (eg, simple excision, tooth extraction) within 5 days before first dose of study treatment. Complete wound healing from major or minor surgery must have occurred at least prior to first dose of study treatment. * Note: Fresh tumor biopsies should be performed at least 5 days before the first dose of study treatment. Participants with clinically relevant ongoing complications from prior surgical procedures, including biopsies, are not eligible. * Corrected QT interval calculated by the Fridericia formula (QTcF) \> 480 ms within 14 days per electrocardiogram (ECG) before first dose of study treatment. * Note: Triplicate ECG evaluations will be performed and the average of these 3 consecutive results for QTcF will be used to determine eligibility. * History of psychiatric illness likely to interfere with ability to comply with protocol requirements or give informed consent. * Inability to swallow tablets. * Previously identified allergy or hypersensitivity to components of the study treatment formulations. * Other conditions, which in the opinion of the Investigator, would compromise the safety of the participant or the participant's ability to complete the study. * Prior treatment toxicities not resolved to ≤ Grade 2 according to the NCI CTCAE Version 5.0.