Study of Olaparib Maintenance Following Cabazitaxel-Carbo in Men With AVPC

Inclusion Criteria: 1. Provision of informed consent prior to any study specific procedures. 2. Provision of informed consent for genetic research. If a patient declines to participate in the genetic research, there will be no penalty or loss of benefit to the patient. The patient will not be excluded from other aspects of the study described in this Clinical Study Protocol, so long as they consent to that part. 3. Patients must agree to tissue collection for correlative studies at the specified timepoints. If patient has undergone a recent tissue collection without intervening treatment since, that can be retrieved and is deemed of sufficient quantity by the PI to undertake the proposed correlative studies, it may be used as the baseline. 4. Male aged 18 years and above. 5. Histologically or cytologically confirmed prostate carcinoma. 6. Presence of metastatic disease documented on imaging studies (bone scan, computed tomography (CT) and/or magnetic resonance imaging (MRI) scans). 7. Patients must meet at least one of the following AVPC criteria: i. Histologically proven small cell (neuroendocrine) prostate carcinoma ii. Exclusive visceral metastases. iii. Predominantly lytic bone metastases identified by plain x-ray or CT scan. iv. Bulky (\>/= 5cm in longest dimension) lymphadenopathy or high-grade tumor mass in prostate/pelvis. v. Low PSA (\</= 10ng/mL) at initial presentation (prior to androgen ablation or at symptomatic progression in the castrate-setting) plus high volume (\>/= 20) bone metastases. vi. Elevated serum lactate dehydrogenase (\>/=2 x upper limit of normal) or elevated serumcarcinoembryonic antigen (\>/= 2 x upper limit of normal ) in the absence of other etiologies. vii. Short interval (\</= 180 days) to castrate-resistant progression following initiation of hormonal therapy. viii. Known loss or mutation (by CLIIA certified molecular testing, IHC and/or DNA sequencing) in at least 2 of the following: Tp53, RB1 and PTEN. 8. (continued from Inclusion Criteria #7: viiii. Patients who have castration -resistant disease progression per RECIST but do not meet PCWG3 PSA progression criteria 9. Patients must have documented evidence of progressive disease as defined by any of the following: a) PSA progression: minimum of 2 rising values (3 measurements) obtained a minimum of 7 days apart with the last result being at least \>/= 1.0 ng/mL; b) New or increasing non-bone disease (RECIST); c) Positive bone scan with 2 or more new lesions (PCWG3). d) Increasing symptoms unequivocally attributed to disease progression as judged by the treating physician and the PI. 10. Surgically or ongoing medically castrated, with baseline testosterone levels of \</= 50 ng/dL \</= 2.0 nM). 11. Eastern Cooperative Oncology Group (ECOG) Performance Status of \</=2. 12. Patients must have normal organ and bone marrow function measured within 7 days prior to administration of study treatment as defined below: i. Hemoglobin \>/= 10.0 g/dL dL (unless due to bone marrow infiltration by tumor, in which case hemoglobin \>/=8gdL is allowed). Patient may have blood transfusions prior to study enrollment. ii. Absolute neutrophil count (ANC) \>/= 1.5 x 10\^9/L (unless due to bone marrow infiltration by tumor, in which case ANC \>1,000/mm3 is allowed) iii. White blood cells (WBC) \>3x10\^9/L (unless due to bone marrow infiltration by tumor, in which case WBC \>2x109/L is allowed) iv. No features suggestive of myelodysplastic syndrome/acute myeloid leukemia on peripheral blood smear v. Platelet count \>/= 100 x 10\^9/L (unless due to bone marrow infiltration by tumor, in which case platelet \>/=50,000/ mm3 is allowed) vi. Total bilirubin \</=1.5 x institutional upper limit of normal (ULN) (except for patients with known Gilbert's disease). 13. (continued from Inclusion Criteria #11 vii. aspartate aminotransferase (serum glutamine oxaloacetic transminase) and alanine aminotransferase (serum glutamic pyruvic transaminase) \</= 2.5 x institutional upper limit of normal (unless liver metastases are present in which case it must be \</= 5x ULN) viii. Calculated creatinine clearance (Cockcroft-Gault Equation) \>/= 40 mL/min. 14. Able to swallow study drugs whole as a tablet/capsule. 15. Patients who have partners of childbearing potential (e.g. female that has not been surgically sterilized or who are not amenorrheic for \>/= 12 months) must be willing to use a method of birth control in addition to adequate barrier protection as determined to be acceptable by the investigator during the study and for 13 weeks after last study drug administration. Please note that the efficacy of hormonal contraception may be decreased if administered with olaparib. 16. 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: 1. Involvement in the planning and/or conduct of the study (applies to both AstraZeneca staff and/or staff at MD Anderson) 2. Previous enrolment or randomization in the present study 3. Any prior treatment for castration-resistant prostate cancer (CRPC) with carboplatin, cisplatin, cabazitaxel or olaparib. 4. Patients whose disease is refractory (defined as evidence of disease progression while on drug or within 3 months of its discontinuation) to more than 2 lines of chemotherapy given for CRPC. Any number of chemotherapies to which the patient's disease is not refractory are allowed, as long as time on treatment did not exceed 6 months (counted from day 1 of cycle 1 to day 1 of the last cycle of treatment). 5. Patients who have not recovered from adverse events secondary to systemic therapy (except for luteinizing hormone-releasing (LHRH) hormone agonist or antagonist treatment for prostate cancer, and bisphosphonates or receptor activator of Nf kappa (RANK) ligand inhibitors for bone strengthening), major surgery or radiotherapy for the treatment of prostate cancer to a grade \</= 2. 6. Persistent toxicities (\>/= common terminology criteria for adverse events grade 2) with the exception of alopecia, caused by previous cancer therapy. 7. Chronic use of known strong CYP3A4 inhibitors (e.g. ketoconazole, itraconazole, ritonavir, indinavir, saquinavir, telithromycin, clarithromycin, voriconazole, nefazodone, posaconazole, ritonavir, lopinavir/ritonavir, indinavir, saquinavir, boceprevir, telaprevir and nelfinavir), moderate CYP3A4 inhibitors (e.g. amprenavir, aprepitant, atazanavir, ciprofloxacin, crizotinib, darunavir/ritonavir, diltiazem, erythromycin, fluconazole, fosamprenavir, imatinib, verapamil), strong CYP3A4 inducers (e.g. phenytoin, rifampicin, carbamazepine, St.John's Wort, phenobarbital) and moderate CYP3A4 inducers (e.g. bosentan, efavirenz, etravirine, modafinil and nafcillin). Concomitant use of these drugs with olaparib is not allowed. Patients may undergo limited courses of them prior to starting olaparib but will be required to have \>/= 5 week washout period from phenobarbital, and \>/=3 week washout period from the rest, before randomization. 8. Active uncontrolled infection ( patients completing a course of antibiotic or antiviral therapy whose infection is deemed to be controlled may be allowed on study after discussion with the PI; the PI will serve as the final arbiter regarding eligibility). 9. Active or symptomatic viral hepatitis or chronic liver disease. 10. A diagnosis or suspicion of myelodysplastic syndrome/acute myeloid leukemia. 11. A history of pneumonitis or extensive bilateral lung disease of non-malignant etiology. 12. A malignancy \[other than the one treated in this study\] which required radiotherapy or systemic treatment within the past 5 years, or has a \>/= 30% probability of recurrence within 24 months (except for adequately treated non-melanoma skin cancer, curatively treated in-situ cancer of the Ta urothelial carcinomas). 13. Any underlying medical or psychiatric condition, which in the opinion of the Investigator, will make the administration of study drug hazardous or obscure the interpretation of adverse events. Examples include, but are not limited to, uncontrolled ventricular arrhythmia, recent (within 3 months) myocardial infarction, superior vena cava syndrome, extensive bilateral lung disease on high-resolution computed tomography scan, uncontrolled seizures or any psychiatric disorder that prohibits obtaining informed consent. 14. Patients unable to swallow orally administered medication and patients with gastrointestinal disorders likely to interfere with absorption of the study medication. 15. Patients with symptomatic uncontrolled brain metastases or spinal cord compressions. A scan to confirm the absence of brain metastases is not required. The patient can receive a stable dose of corticosteroids before and during the study as long as these were started at least 28 days prior to treatment. 16. Patients with a known hypersensitivity to the olaparib, carboplatin or cabazitaxel. 17. Prisoners or subjects who are involuntarily incarcerated. 18. Subjects who are compulsorily detained for treatment of either a psychiatric or physical (e.g. infectious disease) illness.