Docetaxel and Carboplatin for Patients With mCRPC and DNA-Repair Deficiencies

Inclusion Criteria Patients meeting the following inclusion criteria will be eligible to participate in this study: 1. Signed informed consent form (ICF) providing agreement to adhere to the dosing schedule, report for all trial visits and authorization, use and release of health and research trial information. 2. Age \> 18 years 3. Known prostate cancer 4. Ongoing gonadal androgen deprivation therapy with gonadotropin-releasing hormone (GnRH) analogues, antagonists or orchiectomy. Patients who have not had an orchiectomy must be maintained on effective GnRH analogue/antagonist therapy. 5. Castration resistant prostate cancer as defined by serum testosterone \< 50ng/ml and one of the following: * PSA level of at least 2 ng/ml that has risen on at least 2 successive occasions at least 1 week apart. * Evaluable disease progression by modified RECIST (Response Evaluation Criteria in Solid Tumors). * Progression of metastatic bone disease on bone scan with \> 2 new lesions. 6. Prior therapy with abiraterone acetate, enzalutamide, or docetaxel. There is no limit to the number of prior treatment regimens. 7. Presence of metastatic disease on scans. 8. Eastern Cooperative Oncology Group (ECOG) Performance Status of ≤ 2. 9. Life expectancy \>12 weeks. 10. No prior malignancy is allowed except: * Adequately treated basal cell or squamous cell skin cancer or * In situ carcinoma of any site or * Other adequately treated malignancy for which the patient has been disease-free for at least one year (any prior chemotherapy is allowed). 11. Patients must have adequate organ and marrow function as defined below obtained within 14 days prior to start of therapy: 1. Absolute neutrophil count \>1.5 x 109 cells/L 2. Hgb \> 9.0 g/dL 3. Platelets \>100,000 x 109/L 4. Aspartate aminotransferase (AST), alanine aminotransferase (ALT), and total bilirubin levels \< 1.5 x Upper Limit of Normal (ULN) 12. Presence of germline inactivation of BRCA1, BRCA2, ATM OR one of the following: * Patients with clearly deleterious germline mutations of other genes involved in homologous DNA repair may be included at the investigator's discretion. * Patients with homozygous inactivation of genes involved in homologous recombination from primary or metastatic tumor as assessed by a Clinical Laboratory Improvement Amendments (CLIA) level assay for DNA sequencing may be included. * Patients with a signature of homologous recombination deficiency in primary or metastatic tissue may be included (VA Puget Sound only). Exclusion Criteria Patients who meet any of the following criteria will be excluded from the study: 1. Currently receiving active therapy for other neoplastic disorders. 2. Histologic evidence of small cell carcinoma (morphology alone - immunohistochemical evidence of neuroendocrine differentiation without morphologic evidence is not exclusionary). 3. Prior treatment with platinum-based chemotherapy for prostate cancer. 4. Known parenchymal brain metastasis. 5. Active or symptomatic viral hepatitis or chronic liver disease. 6. Clinically significant heart disease as evidenced by myocardial infarction, or arterial thrombotic events in the past 6 months, severe or unstable angina, or New York Heart Association (NYHA) Class II-IV heart disease or cardiac ejection fraction measurement of \< 35 % at baseline, if done. 7. Treatment with an investigational therapeutic within 30 days of Cycle 1. 8. Patients with dementia/psychiatric illness/social situations limiting compliance with study requirements or understanding and/or giving of informed consent are not eligible 9. Any medical conditions, which, in the opinion of the investigators, would jeopardize either the patient or the integrity of the data obtained are not eligible.