• Must be willing to provide informed consent prior to any study specific procedures

• Documented histologically confirmed adenocarcinoma of the prostate

• Patient must have evidence of castration resistant prostate cancer as evidenced by PSA progression (per Prostate Cancer Working Group 3 \[PCWG3\] criteria) and a castrate serum testosterone level (i.e., ≤ 50 mg/dL)

• PSA must be at least 1 ng/ml and rising on two successive measurements at least two weeks apart

• Patients must have progressed on abiraterone and/or enzalutamide; there must be at least a 3-week washout period after stopping the most recent approved therapy for mCRPC (i.e., abiraterone, enzalutamide, Ra-223, sipuleucel-t); if applicable, patients should be weaned off steroids at least 1 week prior to starting treatment

• No prior chemotherapy for the treatment of mCRPC; patients may have received docetaxel for the treatment of hormone-sensitive prostate cancer

• Prior treatment with non-chemotherapy investigational agents is permitted; there must be at least a 3-week washout period after stopping any investigational cancer agent

• Hemoglobin ≥ 10.0 g/dL with no blood transfusion in the past 28 days (within 28 days prior to administration of study treatment)

• Absolute neutrophil count (ANC) ≥ 1.5 x 10\^9/L (within 28 days prior to administration of study treatment)

• Platelet count ≥ 100 x 10\^9/L (within 28 days prior to administration of study treatment)

• Total bilirubin ≤ 1.5 x institutional upper limit of normal (ULN) (within 28 days prior to administration of study treatment)

• Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamic pyruvate transaminase \[SGPT\]) ≤ 2.5 x institutional upper limit of normal unless liver metastases are present in which case they must be ≤ 5 x ULN (within 28 days prior to administration of study treatment)

• Patients must have creatinine clearance estimated using the Cockcroft-Gault equation or based on a 24 hour urine test of ≥ 51 mL/min (within 28 days prior to administration of study treatment)

• Eastern Cooperative Oncology Group (ECOG) performance status 0-1

• Patients must have a life expectancy ≥ 16 weeks

• Male patients and their partners, who are sexually active and of childbearing potential, must agree to the use of two highly effective forms of contraception in combination throughout the period of taking study treatment and for 3 months after last dose of study drug(s) to prevent pregnancy in a partner

• Patient is willing and able to comply with the protocol for the duration of the study including undergoing treatment and scheduled visits and examinations

• At least one lesion (measurable and/or non-measurable) that can be accurately assessed at baseline by computed tomography (CT), positron-emission tomography (PET), magnetic resonance imaging (MRI) and/or bone scan and is suitable for repeated assessment

• Must have archival tissue available, be willing to undergo metastatic biopsy or have a sufficient plasma circulating tumor DNA (ctDNA) concentration in order to perform next-generation DNA sequencing

• The study will require that 50% of enrolled subjects have homozygous deletions, deleterious mutations, or both in one or more of the DNA damage response (DDR) genes; the other 50% of patients must have an intact DDR pathway