Abiraterone Acetate and Antiandrogen Therapy With or Without Cabazitaxel and Prednisone in Treating Patients With Metastatic, Castration-Resistant Prostate Cancer Previously Treated With Docetaxel

Inclusion Criteria: * Histologically confirmed diagnosis of prostate cancer (adenocarcinoma of the prostate) * Previous chemotherapy with at least 3 cycles of docetaxel for hormone-sensitive metastatic prostate cancer * Metastatic disease as evidenced by the presence of soft tissue and/or bone metastases on imaging studies (CT/magnetic resonance imaging \[MRI\] of abdomen/pelvis, bone scintigraphy or NaF PET/CT) * Ability to swallow abiraterone acetate tablets as a whole * All patients must be receiving standard of care androgen deprivation treatment (surgical castration versus LHRH agonist or antagonist treatment); subjects receiving LHRH agonist or antagonist must continue treatment throughout the time on this study * Patients must have castrate serum level of testosterone of \< 50 ng/dL (\< 1.73 nmol/L) * Patients must have progressive disease while receiving androgen deprivation therapy defined by any one of the following as per the Prostate Cancer Clinical Trials Working Group 3 (PCWG3) criteria for PSA, measurable disease or non-measurable (bone) disease during treatment with ADT: * PSA: At least two consecutive rises in serum PSA, obtained at a minimum of 1-week intervals, with the final value \>= 1.0 ng/mL, confirmed \<=4 weeks prior to randomization * Measurable disease (by RECIST 1.1): \> 20% increase in the sum of the longest diameters of all measurable lesions or the development of new measurable lesions; the short axis of a target lymph node must be more th…