Inclusion Criteria:  Able to provide written informed consent Adult (age ≥ 18 years) Histologically confirmed diagnosis of carcinoma of the prostate  Documented progressive mCRPC based on at least one of the following criteria:  PSA progression, defined as at least 2 rises in PSA with a minimum of a 1 week interval (1.0 ng/mL is the minimal starting value if confirmed rise is the only indication of progression) Soft-tissue progression per RECIST 1.1 Progression of bone disease (evaluable disease) or 2 or more new bone lesions by bone scan Progression after treatment with at least 2 prior lines of anticancer therapy approved for treatment of metastatic prostate cancer; prior treatment of subjects in Cohort D (MSI-H or MMRD) must include a checkpoint inhibitor approved by FDA for that indication Subjects who did not have a surgical orchiectomy must be on androgen suppression treatment (eg, luteinizing hormone-releasing hormone agonist) with castrate level of testosterone (≤ 50 ng/dL) and be willing to continue the treatment throughout the study  Prior targeted or whole exome sequencing panel performed by CLIA-certified laboratory documenting:  Cohort A (AVPCa) - Aggressive variant prostate cancer Cohort B or C (HRD) - Homologous recombination deficient (HRD) tumor Cohort D (MSI-H/MMRD) - Microsatellite instability-high (MSI-H) or mismatch repair deficient (MMRD) tumors (MSI-H/MMRD) Cohort E (No Targetable Mutations) - Not eligible for Cohorts A, B, C, or D Evaluable disease according to PCWG3 criteria Adequate archival metastatic tumor tissue or agree to undergo a biopsy of at least 1 metastatic site (fresh biopsy of primary prostate is only allowed if there is clear local disease and no other measurable disease site or biopsiable bone lesion) ECOG performance status of 0 or 1 Able and willing to complete the study according to the study schedule  Exclusion Criteria:  Currently receiving anticancer therapies other than androgen deprivation therapy  Treatment with any other anticancer therapy within 2 weeks of the start of study drug (ie, other immunotherapy, chemotherapy, radiation therapy, etc.) Prior treatment with any cytotoxic T-lymphocyte-associated protein (CTLA4), PD1, PDL1, or programmed cell death ligand 2 (PDL2) directed immunotherapy, except subjects in Cohort D, who will have had prior FDA-approved checkpoint inhibitor therapy Grade 4 immune-mediated adverse events related to prior immunotherapy (applicable to subjects eligible for Cohort D) Failure to recover from any toxicity related to previous anticancer treatment to ≤ Grade 2 Have known active central nervous system metastases and/or carcinomatous meningitis. Subjects with previously treated brain metastases may participate provided they are radiologically stable, ie, are without evidence of progression for at least 4 weeks by repeat imaging (note that the repeat imaging should be performed during study screening), are clinically stable, and are without requirement of steroid treatment for at least 14 days prior to first dose of study treatment. Platelet count < 100 × 109/L Hemoglobin level ≤ 9.0 g/dL Absolute neutrophil count ≤ 1.7 × 109 for subjects who will receive cabazitaxel; < 1.0 × 109/L for all others Aspartate aminotransferase at screening > 3 × upper limit of normal (ULN) for subjects without known liver involvement by tumor or > 5 × ULN for subjects with known liver involvement by tumor Alanine aminotransferase at screening > 3 × ULN for subjects without known liver involvement by tumor or > 5 × ULN for subjects with known liver involvement by tumor Bilirubin ≥ 1.5 × ULN (unless prior diagnosis and documentation of ongoing hemolysis or Gilbert's syndrome has been made) Estimated creatinine clearance < 50 mL/minute calculated by the Cockcroft Gault or Modification of Diet in Renal Disease formulas Active known or suspected autoimmune disease (except vitiligo; type 1 diabetes mellitus or residual hypothyroidism due to an autoimmune condition that is treatable with hormone replacement therapy only; psoriasis, atopic dermatitis, or another autoimmune skin condition that is managed without systemic therapy; or arthritis that is managed without systemic therapy beyond oral acetaminophen and nonsteroidal anti-inflammatory drugs) Have any condition requiring systemic treatment with corticosteroids, prednisone equivalents, or other immunosuppressive medications within 14 days prior to first dose of study drug (except inhaled or topical corticosteroids or brief courses of corticosteroids given for prophylaxis of contrast dye allergic response). Subjects who are currently taking prednisone from a previous prostate cancer therapy will be permitted to enroll in the study. Receipt of an organ allograft Known history of left ventricular ejection fraction ≤ 40% History or evidence of any other clinically unstable/uncontrolled disorder, condition, or disease other than their primary malignancy that, in the opinion of the Investigator, would pose a risk to patient safety or interfere with study evaluations, procedures, or completion Evidence of any serious bacterial, viral, parasitic, or systemic fungal infections within the 30 days prior to the first dose of study drug Receipt of a live-virus vaccine within 30 days prior to the first dose of study drug (seasonal flu vaccines that do not contain live virus are permitted) A human immunodeficiency virus (HIV) positive subject with CD4+ T-cell (CD4+) counts < 350 cells/μL, or an HIV viral load greater than 400 copies/mL, or a history of an AIDS (acquired immunodeficiency syndrome)-defining opportunistic infection within the past 12 months, or who has not been on established antiretroviral therapy (ART) for at least 4 weeks prior to initiation of study drug dosing. (Effective ART is defined as a drug, dosage, and schedule associated with reduction and control of the viral load.) Positive test for hepatitis C RNA (a subject who is hepatitis C virus [HCV] antibody positive but HCV RNA negative due to documented, curative prior antiviral treatment or natural resolution is eligible) Positive test for hepatitis B surface antigen (HBsAg) or hepatitis B core antibody (HBcAb; a subject whose HBsAg is negative and HBcAb is positive may be enrolled if a hepatitis B virus [HBV] DNA test is negative and the subject is retested for HBsAg and HBV DNA every 2 months)