Abiraterone/Prednisone, Olaparib, or Abiraterone/Prednisone + Olaparib in Patients With Metastatic Castration-Resistant Prostate Cancer With DNA Repair Defects

Inclusion Criteria: * Ability to understand and the willingness to sign a written informed consent document that is approved by the local institutional review board and HIPAA authorization for the release of personal health information. * Histological or cytological proof of prostate adenocarcinoma (Note: small-cell carcinoma of the prostate is not permitted) * Documented progressive mCRPC based on at least one of the following criteria: 1. PSA progression defined as 25% increase over baseline value with an increase in the absolute value of at least 2.0 ng/mL that is confirmed by another PSA level with a minimum of a 1 week interval and a minimum PSA of 2.0 ng/mL. 2. Progression of bidimensionally measurable soft tissue or nodal metastasis assessed within one month prior to registration by a CT scan or MRI. 3. Progression of bone disease (evaluable disease) (new bone lesion(s)) by bone scan. * Agree to undergo a biopsy of at least one metastatic site (fresh biopsy of primary prostate only allowed if there is clear local disease and no other measurable disease site or biopsiable bone lesion.) to determine DNA repair defects. (Please refer to the Laboratory Manual for specific procedures). However: 1. Adequate archival metastatic or primary disease tumor tissue can be used if available in lieu of a new biopsy. These patients will only be eligible for protocol therapy if the biopsy has tumor that is positive for DNA repair defects. 2. Patients with known DNA damage repair defects based on prior appropriately validated metastatic or prostate tissue analysis may be used in lieu of new biopsy/analysis based on central site evaluation of quality of the biopsy and analysis. 3. Patients with known germline DNA repair defects are eligible without a biopsy. However it will be highly desirable that they undergo a metastatic (or fresh prostate biopsy if there is clear local disease and no other measurable disease site or biopsiable bone lesion) disease biopsy to better define the scope of the DNA repair defects in the current disease context. * ECOG status of 0-2 (Appendix A: Performance Status Criteria). * Adequate organ function as defined below obtained within 14 days of registration: ANC \> or = 1500/µl Hemoglobin ≥ 10.0 g/dL WBC \> 3x10\^9/L Platelet count 100,000/µl Creatinine ≥51 mL/min estimated using the Cockcroft-Gault equation Potassium ≥ 3.5 mmol/L (within institutional normal range) Bilirubin within normal institutional limits (or \<2X the upper limit of normal (ULN) in those with Gilbert's disease) AST (SGOT) / ALT (SGPT) ≤ 1.5x institutional ULN unless liver metastases are present in which case it must be ≤ 5x ULN * The effects of abiraterone, olaparib or the combination of both on the developing human fetus at the recommended therapeutic dose are unknown. Men must agree to use adequate contraception prior to study entry, for the duration of study participation and for at least 3 months thereafter. * Patients must discontinue antiandrogen therapy (i.e., flutamide, bicalutamide, nilutamide) for at least 4 weeks prior to registration with no evidence of a falling PSA after washout. * Serum testosterone \< 50 ng/dL. Patients must continue primary ADT with an LHRH analogue (agonist or antagonist) if they have not undergone orchiectomy. * Able to take oral medication without crushing, dissolving or chewing tablets. * Patients must have a life expectancy ≥ 6 months. * Patients may have received prior radiation therapy or surgery. However, at least 14 days must have elapsed since completion of radiation therapy or surgery and patient must have recovered from all side effects at the time of registration (e.g. back to baseline or grade 1) . * Patient is willing and able to comply with the protocol for the duration of the study including undergoing treatment and scheduled visits and examinations including follow up. Exclusion Criteria: * Prior exposure to CYP17 (other than ketoconazole) or PARP inhibitors for prostate cancer. Patients with prior exposure to ketoconazole are eligible. * Prior chemotherapy for castration resistant disease. Chemotherapy given in the hormone-sensitive setting is permissible if stopped at least 4 weeks prior to registration. Note: Patients can receive a stable dose of bisphosphonates for bone metastases, including zoledronic acid, or denosumab before and during the study as deemed appropriate by the treating physician. * Prior exposure to enzalutamide, ARN-509 or other investigational AR-directed therapy in the setting of mCRPC. * Patients with a currently active second malignancy excluding non-melanomatous skin cancer or superficial transitional cell carcinoma. Note: Patients are not considered to have a "currently active" malignancy if they have completed all therapy and are now considered without evidence of disease for 1 year. * Patients receiving any other investigational agents. Any prior investigational agents must be stopped at least 14 days (2 week washout) prior to registration. * Patients who have received itraconazole, ketoconazole, or fluconazole within 3 weeks prior to registration or those who have not recovered (i.e., back to baseline or Grade 1) from AEs due to agents administered more than 3 weeks earlier. * Patients with a history of active seizures (or a single confirmed seizure event) in the last 2 years from the time of registration. * Patients with a history of pituitary or adrenal dysfunction or active or symptomatic viral hepatitis or chronic liver disease are not eligible. * Patients with active brain metastases. A scan to confirm the absence of brain metastases is not required for asymptomatic patients. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to olaparib or abiraterone. * Patients considered a poor medical risk due to a serious, uncontrolled medical disorder, non-malignant systemic disease or active, uncontrolled infection. Examples include, but are not limited to, uncontrolled ventricular arrhythmia, recent (within 3 months) myocardial infarction, unstable spinal cord compression (untreated or unstable within at least 28 days prior to registration), superior vena cava syndrome, and extensive bilateral lung disease on HRCT scan or any psychiatric disorder that prohibits obtaining informed consent. * Patients with prolonged pre-existing hematological toxicities including known indicators of bone marrow failure or abnormality. * Patients with myelodysplastic syndrome / acute myeloid leukemia. * Patients may continue on a daily Multi-Vitamin, calcium and Vitamin D, but all other herbal, alternative and food supplements (i.e. PC-Spes, Saw Palmetto, St John's Wort, etc.) must be discontinued before starting protocol treatment. Hormonal-acting agents such as DES are forbidden during the trial and must be stopped prior to starting protocol treatment. No washout period will be required. Patients on megesterol acetate for hot flashes are allowed to continue therapy. * Patients must stop taking ritonavir, idinavir, saquinavir, telithromycin, clarithromycin and nelfinavir 1 week prior to registration. Note: topical ketoconazole is permitted. * Patients must stop taking phenytoin, rifampicin, rifapentine, rifabutin, carbamazepine, nevirapine, modafinil and St John's Wort (Hypericum perforatum) 3 weeks prior to registration. Patients must stop taking phenobarbitone 5 weeks prior to registration. Patients must stop taking all strong CYP3A4 inhibitors, including clarithromycin, telithromycin, nefazodone, itraconazole, ketoconazole, atazanavir, darunavir, indinavir, lopinavir, nelfinavir, ritonavir, saquinavir, and tipranavir, prior to registration. * Patients must not be planning to receive any concurrent cytotoxic chemotherapy, surgery or radiation therapy during protocol treatment. * Use of any prohibited concomitant medications within 7 days of registration. * Patients who are HIV-positive on combination antiretroviral therapy because of the potential for pharmacokinetic interactions with olaparib. In addition these patients are at increased risk of lethal infections when treated with marrow suppressive therapy. * Patients with known active Hepatitis B or Hepatitis C. * Patients with baseline moderate to severe hepatic impairment (Child-Pugh Class B and C). * Persistent toxicities (≥CTCAE Grade 2), with the exception of alopecia, caused by previous cancer therapy. * Resting ECG with QTc \> 470msec on 2 or more time points within a 24 hour period or of long QT syndrome. * Patients with significant cardiac history including: * Severe or unstable angina pectoris * Uncontrolled hypertension (defined as systolic BP ≥ 160 mmHg or diastolic BP ≥ 95 mmHg). Note - Patients with a history of hypertension are allowed provided blood pressure is controlled by anti-hypertensive treatment * Atrial fibrillation or other cardiac arrhythmia requiring therapy. * Heart disease as evidenced by myocardial infarction, or aterial thrombotic events in the past 6 months * Class II-IV heart failure (as defined by New York Heart Association) or a cardiac ejection fraction measurement of less than 50% at baseline * Blood transfusion within 30 days of consent. * Previous allogeneic bone marrow transplant. * Major surgery within 14 days of registration and patients must have recovered from any effects of any major surgery. * Patients with any condition likely to interfere with absorption of the study medication. * No other condition which, in the opinion of the Investigator, would preclude participation in this trial. * Patients who have noncanonical DNA repair defects and extensive visceral disease or symptomatic bone disease requiring urgent tumor response.