Study of Abiraterone Acetate and Prednisone in Combination With Cabazitaxel in Patients With Prostate Cancer

Inclusion Criteria: * Written informed consent has been obtained. * Adults over 18 years of age. * Histologically or cytologically proven adenocarcinoma of the prostate. * Stage IV disease as evidenced by soft tissue, visceral and/or bony metastasis must be Response Evaluation Criteria in Solid Tumors (RECIST) evaluable on CT scan and/or bone scan * Progressive disease while receiving hormonal therapy or after surgical castration documented by at least one of the following: 1. Increase in measurable disease per RECIST 1.1, 2. Appearance of new lesions on bone scan consistent with progressive prostate cancer (\>2 new lesions on bone scans if this is the only measure of PD), 3. rising PSA defined as 2 sequential increases above a previous lowest reference value. * Each value must be obtained at least 1 week apart. * PSA at least 2 ng/mL * Received prior docetaxel chemotherapy * Received prior abiraterone acetate, but not within the 3 months prior to study drug dosing. * Testosterone level \<50 ng/mL. Patients receiving Leutinizing Hormone Releasing Hormone (LHRH) agonists or antagonists must be continued to maintain castrate levels of testosterone while on study. * Eastern Cooperative Oncology Group (ECOG) performance status ≤ 2. * Adequate hematologic function: 1. platelet \>100, 000/uL; 2. neutrophil count of \>1500 cell/mm3; 3. hemoglobin \>9.0 g/dL) * Adequate renal function (Creatinine clearance \> 50 mL/min) * Adequate potassium level (\> 3.5 mEq/dL) * Adequate hepatic function 1. bilirubin \< 1.5 X upper limit of normal (ULN), 2. alanine aminotransferase (ALT) \< 1.5 X ULN, 3. aspartate aminotransferase (AST) \< 1.5 X ULN. 4. serum albumin of ≥ 3.0 g/dL. * Controlled blood pressure, defined as blood pressure ≤ 140/90 on average (3 separate readings taken at screening visit in a relaxed clinical environment and averaged) * Must be able to take oral medication without crushing, dissolving or chewing tablets * Willing to take abiraterone acetate on empty stomach; (1) no food should be consumed at least two hours before and for at least one hour after the dose of abiraterone acetate is taken. * Patients must be willing and able to adhere to the prohibitions and restrictions specified in this protocol. * Written authorization for use and release of health and research study information has been obtained. * Patients who have partners of childbearing potential must be willing to use a method of birth control with adequate barrier protection during the study and for 1 week after the last dose of abiraterone acetate. Exclusion Criteria: * Surgery or radiation therapy within 2 weeks, or * Cytotoxic anti-cancer therapy within 3 weeks, or * Non-cytotoxic anti-cancer therapy within 2 weeks, or 5 half-lives (whichever is shorter) of Study Day 1. * Prior radiotherapy to ≥ 40% of bone marrow. * Prior treatment with Radium 223. * Use of an investigational therapeutic agent within 30 days. * Have a history of gastrointestinal disorders (medical disorders or extensive surgery) that may interfere with the absorption of the study agents. * Prior treatment with cabazitaxel. * Known chronic infection with human immunodeficiency virus (HIV). * Known active, or symptomatic, brain metastasis. * Blood pressure \>140/90 on average (3 separate readings taken at screening visit in a relaxed clinical environment and averaged). * History of autoimmune disorder requiring daily corticosteroid therapy of greater than prednisone 10mg daily, or its equivalent. * Baseline peripheral edema \> grade 3. * Pre-existing diarrhea uncontrolled with supportive care; * Prior hemorrhagic diarrhea due to ulcerative colitis, inflammatory bowel disease or other cause; * Active, uncontrolled peptic ulcer disease even in the setting of proton-pump inhibitor or Histamine2-blocker use. * Pre-existing peripheral neuropathy grade \> 2. * Documented hypersensitivity (CTCAE grade \> 2) to any drug containing polysorbate 80. * Have known allergies or hypersensitivity to abiraterone acetate or prednisone or their excipients. * Contraindications to steroid use. * Need for medications that strongly induce or inhibit cytochrome P450 3A4 (CYP3A4) or cytochrome P450 2D6 (CYP2D6) activity. (see section 7.2.3 for details) * Serious infection requiring parenteral antibiotics within 14 days of enrollment. * Poorly controlled diabetes (Hgb A1C \>9). * Active or symptomatic viral hepatitis or Chronic liver disease, including Child-Pugh Class B and C liver disease. * History of pituitary or adrenal dysfunction. * Clinically significant heart disease as evidenced by: 1. myocardial infarction, or 2. arterial thrombotic events in the past 6 months, 3. severe or unstable angina, or 4. New York Heart Association Class III-IV heart disease, or 5. cardiac ejection fraction measurement of \<50% at baseline. * Consumption of food or beverages containing grapefruit juice within 7 days of study drug dosing * Use of a first-generation anti-androgen such as: 1. bicalutamide within 6 weeks of study drug dosing, or 2. flutamide within 4 weeks of study dosing. * Have any condition that, in the opinion of the investigator, would compromise the well-being of the subject or the study or prevent the subject from meeting or performing study requirements.