Carboplatin or Olaparib for BRcA Deficient Prostate Cancer

Study General Trial Over-view This study is designed to help better understand treatment options compared to standard therapies for patients who have targeted DNA repair mutations and metastatic castrate resistant prostate cancer (mCRPC). Cancer therapies are aimed at finding a way to kill the cancer cells while causing minimal damage to normal (non-cancer) cells. This often works because cancers cells grow faster than many normal cells, many treatments are aimed at to take advantage of that difference. One of the ways to do this is to damage the DNA of these more rapidly growing cells. However, if the cells have a way of repairing that damage then therapies may not work as well. Some research shows that when specific changes or mutations occur in the genes involved with repairing DNA damage, resulting cancers have responded well to drugs which damage DNA. Olaparib is known as a PARP inhibitor and is standard of care therapy for men with BRCA altered mCRPC. Carboplatin is a synthetic antineoplastic agent which has been used in the treatment of solid tumors and BRCA related cancers. When mutations occur in critical DNA-repair genes, research has found that treatment with carboplatin is also effective. This research is being done to determine the response of mCRPC in patients with DNA repair mutations to treatment with olaparib compared to carboplatin. This study will test whether giving one drug or the other a has a better response. Patients wishing to participate in this study are screened for safety and health eligibility before enrolling. This study is enrolling 100 male participants total, from across the VAMC nationally who have the following: * Metastatic castration-resistant prostate cancer (mCRPC) * Cancer that has gotten worse, after any number of first-line treatments * Mutations in DNA-repair genes discovered as part of a patient's routine care. Once eligibility is determined, enrolled participants are randomized into one of two groups: * Group A will start with carboplatin (IV) first, given every 21 days, then have the option to switch to the second treatment with olaparib taken daily, (orally) with cycles of every 28 days. * Group B will start with olaparib first, taken (orally), with 28 day cycles, then have the option to switch to the second treatment with carboplatin (IV) every 21 days. Both study drugs in this trial are currently FDA approved, and are prescribed at the participating VAMC clinical sites per institutional guidelines. Carboplatin given in IV is also given as prescribed at the participating VAMC, and administered per institutional guidelines. Participants are monitored for health and body function, cancer progression, toxicity and life quality at every visit during the trial and at an end of treatment visit (28 days after completion of the trial or after withdrawal). For participants who respond well to treatment during the trial, additional treatment cycles may be added and the study can be extended. Participants who experience intolerable toxicity, cancer progression, or whose doctors decide to change treatment, will either be switched to the opposite study drug or withdrawn from the study. This important trial is designed to compare response rate and duration of response using carboplatin compared to olaparib in patients who have mCRPC which contains DNA repair gene mutations.