Study of Cabozantinib and Nivolumab in Metastatic Castration Resistant Prostate Cancer

Inclusion Criteria: Subjects must meet all of the following applicable inclusion criteria to participate in this study: * Willing and able to provide, or have a legally authorized representative provide, written informed consent and HIPAA authorization for the release of personal health information. A signed informed consent must be obtained before screening procedures are performed. NOTE: HIPAA authorization may be either included in the informed consent or obtained separately. * Males 18 years of age and above. * Histological or cytological proof of prostate adenocarcinoma or mixed adenocarcinoma/neuroendocrine tumors. Pure small cell of the prostate is not allowed. * ECOG status of ≤ 2 * Progressive mCRPC as defined: 1) castrate levels of serum testosterone \< 50 ng/dL AND 2) progressive disease as defined by PSA or radiographic progression. Subjects with measurable and non-measurable disease (i.e., bone only metastases) are allowed. NOTE: ENROLLMENT of subjects with non-measurable disease (i.e., bone only metastases) will be capped at 50% of enrollment target (n=25). * Must have exposure to one prior taxane (or be taxane ineligible or refuse taxane) AND one prior AR-targeting agent (for example, abiraterone, enzalutamide, apalutamide, darolutamide). Receipt of taxane or AR-targeting agent may be in the hormone sensitive or castration resistant setting. Subjects may have received more than 1 prior Androgen receptor signaling inhibitors (ARSI). Subjects may have had prior 177Lu-PSMA-617. * Recovery to baseline or ≤ Grade 1 CTCAE v5.0 from toxicities related to any prior treatments, unless AE(s) are clinically nonsignificant and/or stable on supportive therapy. * Normal organ function with acceptable initial laboratory values within 14 days of treatment start: * WBC: ≥ 2,500/mcL * ANC: ≥ 1,500/mcL * Hemoglobin: ≥ 9 g/dL (transfusions are permitted) * Platelet count: ≥ 100,000/mcL * Serum creatinine or calculated Creatinine Clearance: Serum creatinine ≤ 1.5 x ULN or calculated CrCl ≥ 30 mL/min as defined by Cockcroft-Gault equation * Total Bilirubin: ≤ 1.5 x ULN (≤ 3 x ULN for subjects with documented Gilbert's disease) * SGOT (AST): ≤ 3 x ULN * SGPT (ALT): ≤ 3 x ULN * Alkaline Phosphatase (ALP): ≤ 5 x ULN with documented bone metastases * Serum Albumin: ≥ 2.8 g/dL * Urine protein/creatinine ratio (UPCR): ≤ 2 mg/mg (≤ 113.2 mg/mmol), or 24-h urine protein ≤ 2 g * Subjects must agree to use a medically acceptable method of birth control as outlined in the protocol * HIV-positive with negative viral loads on stable antiretroviral regimen will be considered eligible. Subjects must have CD4 count \> 350. Exclusion Criteria: Subjects meeting any of the criteria below may not participate in the study: * Disease progression on prior checkpoint inhibitor treatment. * Prior cabozantinib. * 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 investigational systemic anti-cancer agent within 4 weeks before first dose of study treatment. * Treatment with abiraterone, apalutamide, or darolutamide within 2 weeks of treatment initiation. Treatment with investigational prostate cancer directed therapy within 4 weeks of treatment initiation. Treatment with enzalutamide within 4 weeks of treatment initiation. * Receipt of more than 1 line of chemotherapy (including both hormone sensitive and CRPC). First-generation anti-androgen use (such as bicalutamide) will not be tabulated as a line of therapy. * Administration of a live, attenuated vaccine within 30 days prior to first dose of study treatment. * Active autoimmune disease or condition requiring prednisone \>10 mg daily (or equivalent). Physiologic replacement is permitted. Topical, ocular, intra-articular steroids or inhaled corticosteroids are permitted. * Imminent or established spinal cord compression based on clinical and/or imaging findings. * Radiation therapy within 1 week of study treatment start. * Known brain metastases or cranial epidural disease unless adequately treated with radiotherapy and/or surgery (including radiosurgery) and stable for at least 4 weeks prior to first dose of study treatment. * History of idiopathic pulmonary fibrosis, organizing pneumonia, drug-induced pneumonitis, idiopathic pneumonitis, or evidence of active pneumonitis on screening chest CT scan. * Malabsorption syndrome. * Requirement for hemodialysis or peritoneal dialysis. * History of solid organ or allogenic stem cell transplant. * Active hepatitis B/C or positive TB test with active mycobacterial infection requiring systemic treatment. * Active treatment (within 5 days of registration) with coumarin agents (e.g., warfarin), direct thrombin inhibitors (e.g., dabigatran), direct factor Xa inhibitor betrixaban, or platelet inhibitors (e.g., clopidogrel). Allowed anticoagulants are the following: * Prophylactic use of low-dose aspirin for cardio-protection (per local applicable guidelines) and low-dose molecular weight heparins (LMWH). * Therapeutic doses of LMWH or anticoagulation with direct factor Xa inhibitors rivaroxaban, edoxaban, or apixaban in subjects 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 or the tumor. * The subject has uncontrolled, significant intercurrent or recent illness including, but not limited to, the following conditions: * Cardiovascular disorders: * Congestive heart failure New York Heart Association Class 3 or 4, unstable angina pectoris, serious cardiac arrhythmias. * Uncontrolled hypertension defined as sustained blood pressure (BP) \> 150 mm Hg systolic or \> 90 mm Hg diastolic despite optimal antihypertensive treatment. * Stroke (including transient ischemic attack \[TIA\]), myocardial infarction (MI), or other ischemic event, or thromboembolic event (e.g., deep venous thrombosis, pulmonary embolism) within 6 months before first dose of study treatment. * Subjects with a diagnosis of incidental, subsegmental PE or DVT within 6 months are allowed if stable, asymptomatic, and treated with a stable dose of permitted anticoagulation (see exclusion criterion above) for at least 1 week before first dose of study treatment. * Gastrointestinal (GI) disorders including those associated with a high risk of perforation or fistula formation * The subject has evidence of tumor invading the GI tract, active peptic ulcer disease, inflammatory bowel disease (e.g., Crohn's disease), diverticulitis, cholecystitis, symptomatic cholangitis or appendicitis, acute pancreatitis, acute obstruction of the pancreatic duct or common bile duct, or gastric outlet obstruction. * Abdominal fistula, GI perforation, bowel obstruction, or intra-abdominal abscess within 6 months before first dose of study treatment. Note: Complete healing of an intra-abdominal abscess must be confirmed before first dose of study treatment. * Clinically significant hematuria, hematemesis, or hemoptysis of \> 0.5 teaspoon (2.5ml) of red blood, or other history of significant bleeding (e.g., pulmonary hemorrhage) within 12 weeks before first dose of study treatment. * Cavitating pulmonary lesion(s) or known endotracheal or endobronchial disease manifestation. * Lesions invading or encasing any major blood vessels. * Other clinically significant disorders that would preclude safe study participation. * Serious non-healing wound/ulcer/bone fracture. * Uncompensated/symptomatic hypothyroidism. * Moderate to severe hepatic impairment (Child-Pugh B or C). * Major surgery (e.g., laparoscopic nephrectomy, GI surgery, removal or biopsy of brain metastasis) within 2 weeks before first dose of study treatment. Minor surgeries within 10 days before first dose of study treatment. Subjects must have complete wound healing from major surgery or minor surgery before first dose of study treatment. Subjects with clinically relevant ongoing complications from prior surgery are not eligible. * Corrected QT interval calculated by Fridericia formula (QTcF) \>500 ms per electrocardiogram (ECG) within 14 days before first dose of study treatment \[add reference for Fridericia formula\]. NOTE: If a single ECG shows a QTcF with an absolute \>500 ms, two additional ECGs at intervals of approximately 3 min must be performed within 30 min after the initial ECG, and the average of these three consecutive results for QTcF will be used to determine eligibility. * Any other active malignancy at time of first dose of study treatment or diagnosis of another malignancy within 3 years prior to first dose of study treatment that requires active treatment, except for locally curable cancers that have been apparently cured, such as basal or squamous cell skin cancer or superficial bladder cancer. * Known allergy to any of the compounds under investigation. * Inability to swallow tablets.