Ability to swallow abiraterone acetate tablets as a whole Prior exposure to abiraterone acetate or other specific cytochrome P (CYP)- inhibitors; abiraterone acetate given in the castration-sensitive setting is permissible if stopped at least months prior to initial protocol treatment May have received treatment with abiraterone acetate, enzalutamide and/or one prior chemotherapy (docetaxel) Prior exposure to abiraterone acetate, ketoconazole or other specific cytochrome (CYP)- inhibitors Patients with known adrenal insufficiency, or patients receiving treatment with ketoconazole, abiraterone, or aminoglutethimide. Cohort A: Patients must have progressed during treatment with abiraterone Willing to take abiraterone acetate on an empty stomach; no food should be consumed at least two hours before and for at least one hour after the dose of abiraterone acetate is taken. (Note: apalutamide does not have to be taken on an empty stomach) Subject has been on abiraterone for castration-sensitive prostate cancer (CSPC) or castration-resistant prostate cancer (CRPC). Subjects who have received abiraterone for CSPC must have had a response to hormonal therapy, as defined by any decline in PSA, radiographic response and/or clinical benefit after starting hormonal therapy. Subjects who have received abiraterone for CRPC must have responded to abiraterone, defined by any decline in PSA, radiographic response, and/or clinical benefit after starting abiraterone. Avoid concomitant strong CYPA inducers during abiraterone acetate treatment. If a strong CYPA inducer must be co-administered, increase the abiraterone acetate dosing frequency Prior treatment for prostate cancer, including ADT, orchiectomy, antiandrogens, ketoconazole, abiraterone acetate or enzalutamide Willing to take abiraterone acetate on an empty stomach; no food should be consumed at least two hours before and for at least one hour after the dose of abiraterone acetate is taken. Avoid concomitant strong CYPA inducers during abiraterone acetate treatment. If a strong CYPA inducer must be co-administered, increase the abiraterone acetate dosing frequency. Previous use of abiraterone acetate or other investigational CYP inhibitor (e.g., TAK-). Prior use of abiraterone and other hormonal agents used to treat prostate cancer are permitted but abiraterone acetate should be stopped prior to study treatment initiation Documented disease progression (either radiographic or biochemical) on at least novel hormonal therapy (enzalutamide and/or abiraterone acetate/prednisone) for the treatment of metastatic CRPC, irrespective of prior NHT treatment for non castrate prostate cancer or nonmetastatic (M) CRPC. For subjects in Groups B or C, previous use of at least one androgen pathway inhibitor (either abiraterone acetate or enzalutamide) for metastatic CRPC Patient must have disease progression with abiraterone treatment Willing to take abiraterone acetate on an empty stomach (no food should be consumed at least two hours before and for one hour after dosing) Prior use of apalutamide, abiraterone acetate or degarelix Have metastatic castration-resistant prostate cancer, are chemo-nave for mCRPC (however, six cycles of docetaxel are allowed in hormone-sensitive disease), and have progressed on abiraterone treatment (patients may have had prior therapy including sipuleucel-T, radium-, abiraterone, ketoconazole, and/or Tak-); progression on abiraterone is defined as\r\n* Radiologic progression by Response Evaluation Criteria in Solid Tumors (RECIST) . and Prostate Cancer Working Group (PCWG) criteria, or \r\n* PSA progression on abiraterone:\r\n** For responders to abiraterone: % or greater increase and an absolute increase of ng/mL or more from the nadir, confirmed by a second value obtained or more weeks later\r\n** For non-responders to abiraterone: % increase above baseline with an increase in absolute value of ng/mL or more after weeks of treatment Must have had prior abiraterone treatment Have had second-line hormonal therapy (abiraterone, ketoconazole, and/or Tak-, etc.) within two weeks prior to the first dose of study drug; patients require a two-week wash out; patients may continue standard supportive dosing of prednisone and hydrocortisone for abiraterone and ketoconazole, respectively, as needed Greater than prior therapies in metastatic CRPC (including single-agent docetaxel, abiraterone); abiraterone can only be taken pre-chemotherapy For Cohorts A and B, patients must have progressed on prior treatment with enzalutamide or abiraterone acetate + prednisone (by PSA criteria or radiographically) For Cohort A (enzalutamide) and Cohort B (abiraterone acetate): prior treatment with up to additional second line hormone therapies, including ketoconazole is allowed For Cohort A (enzalutamide) and Cohort B (abiraterone acetate): patients who have progressed on both enzalutamide and abiraterone acetate are eligible and post-BAT will be retreated with the last second line agent they had received (e.g. patient receiving abiraterone acetate [abiraterone] then enzalutamide would receive retreatment with enzalutamide post-BAT) For Cohort A (enzalutamide) and Cohort B (abiraterone acetate): patients must be withdrawn from enzalutamide or abiraterone acetate for >= weeks and have documented PSA increase after the withdrawal period For Cohort A (enzalutamide) and Cohort B (abiraterone acetate): patients receiving prednisone in conjunction with abiraterone acetate must be weaned off prednisone prior to starting BAT Avoid concomitant strong CYPA inducers during abiraterone acetate treatment Subjects must have progressed on prior new hormonal agent (e.g. abiraterone acetate and/or enzalutamide) for the treatment of mCRPC. mCRPC that has progressed on at least therapy progression (defined as Prostate Cancer Working Group [PCWG] or at investigators discretion) approved for treatment of mCRPC, one of which must include abiraterone acetate and/or enzalutamide Treatment with abiraterone within weeks prior to study treatment A known hypersensitivity to abiraterone acetate, apalutamide, and prednisone and/or any of their excipients Patients must not have received prior and/or must not have any plans for receiving concomitant therapy with ketoconazole, aminoglutethimide, or abiraterone acetate, or enzalutamide (MDV); concurrent megestrol for hot flashes is allowed Treatment with approved anti-cancer therapy (with the exception of abiraterone) within weeks of study drug. Abiraterone must not be administered within weeks prior to initiation of study treatment For Cohort A: Has received docetaxel for mCRPC. Prior treatment with other chemotherapy for mCRPC is allowed. Up to second-generation hormonal manipulations (e.g., abiraterone acetate and/or enzalutamide) are allowed For Cohort B: Has received prior treatment with either abiraterone acetate or enzalutamide (but not both) in the prechemotherapy mCRPC state. Participants in Cohort B must have received at least weeks of either abiraterone or enzalutamide treatment (but not both) who failed treatment or became intolerant of the drug For Cohort C: Has received prior treatment with abiraterone acetate in the pre-chemotherapy mCRPC state without prior enzalutamide. Participants in Cohort C must have received at least weeks of abiraterone treatment who failed treatment or become intolerant of the drug. Prior cytotoxic chemotherapy, aminoglutethimide, ketoconazole, abiraterone acetate, or enzalutamide for prostate cancer; Able to swallow a whole tablet and take abiraterone acetate on an empty stomach (defined as no food for two hours before and one hour after abiraterone acetate ingestion) Prior demonstrated hypersensitivity, intolerance or allergy to abiraterone acetate, prednisone or their excipients Prior concomitant therapy with ketoconazole, aminoglutethimide or abiraterone acetate or enzalutamide (MDV) or intent to treat with the above. Concurrent megestrol for hot flashes is allowed. Patients who have disease progression during, or after, receiving abiraterone treatment in any setting. Be eligible for treatment with physician's choice of comparator treatment (abiraterone acetate, enzalutamide or docetaxel) Concomitant use of medications that may alter pharmacokinetics of abiraterone (abiraterone acetate) or enzalutamide Dose-escalation: prior treatment with abiraterone acetate; at least weeks must have elapsed from the last dose of abiraterone acetate Expansion cohort only (if conducted in the study): men with mCRPC and disease progression as defined by PCWG within months (primary resistance); or after at least months of treatment (acquired resistance) of starting treatment with abiraterone acetate; at least weeks must have elapsed from the last dose of abiraterone acetate COHORT A: Prior ketoconazole, abiraterone acetate, or enzalutamide for the treatment of prostate cancer Willing to take abiraterone acetate on an empty stomach; no food should be consumed at least two hours before and for at least one hour after the dose of abiraterone acetate is taken Willing to take abiraterone acetate on an empty stomach; no food should be consumed at least two hours before and for at least one hour after the dose of abiraterone acetate is taken, and should be able to swallow tablets whole, without crushing/chewing tablets Prior treatment with abiraterone acetate or enzalutamide Prior use of abiraterone acetate or cytotoxic chemotherapy for prostate cancer Patients who have been treated with abiraterone will be excluded Prior history of CYP inhibitors (e.g., abiraterone acetate, TAK-) and second-generation anti-androgen (e.g., MDV) Willing to take abiraterone acetate on an empty stomach; no food should be consumed at least two hours before and for at least one hour after the dose of abiraterone acetate is taken Willing to take abiraterone acetate on an empty stomach; no food should be consumed at least two hours before and for at least one hour after the dose of abiraterone acetate is taken Prior ketoconazole, abiraterone acetate, or enzalutamide for the treatment of prostate cancer Currently participating in an abiraterone acetate clinical study considered complete and had received at least months of treatment with abiraterone acetate tablets. Prior treatment with abiraterone Megesterol acetate Prior treatment with abiraterone acetate Use of any antineoplastic treatment post-chemotherapy, including but not limited to aminoglutethimide, ketoconozole, abiraterone acetate, Rad-, sipuleucel-T, or enzalutamide. Continuing steroids is permitted. Treatment with abiraterone acetate prior to enzalutamide for metastatic castration - resistant prostate cancer (mCRPC) in the prechemotherapy setting. (Note: Patients who have received concomitant enzalutamide and abiraterone acetate therapies are not excluded). Prior abiraterone treatment completed at least weeks prior to cycle day . Participants must have failed prior abiraterone treatment. Progressive disease (PD) while receiving AR targeted therapy with abiraterone acetate or enzalutamide within months of treatment initiation (? months) by at least one of the following: Prior AR targeted therapy (abiraterone acetate or enzalutamide) must be stopped at least weeks before study treatment. Known history of mineralocorticoid excess or deficiency (not applicable to patients who have already been treated with abiraterone acetate in first line before inclusion). Abiraterone acetate; primary resistance to abiraterone will be defined as:\r\n* No PSA decline\r\n* PSA decline less than % after weeks of abiraterone therapy\r\n* PSA progression within weeks of abiraterone acetate (AA) treatment (by Prostate Cancer Working Group- [PCWG] criteria), after initial response to therapy\r\n* Objective progression, by RECIST criteria for soft tissue lesions and by modified PCWG criteria for bone lesions within weeks of starting abiraterone treatment\r\n* Unequivocal clinical progression (per the treating provider's discretion) within weeks of starting abiraterone treatment Received prior abiraterone acetate, but not within the months prior to study drug dosing Willing to take abiraterone acetate on empty stomach; no food should be consumed at least two hours before and for at least one hour after the dose of abiraterone acetate is taken Treatment with at least months of abiraterone prior to progression Prior therapy with abiraterone, or aminoglutethimide Prior use of ketoconazole, abiraterone acetate or enzalutamide, or participation in a previous clinical trial of ketoconazole, abiraterone acetate or enzalutamide Willing to take abiraterone acetate on an empty stomach; 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 may have received secondary hormonal manipulations (excluding prior abiraterone acetate, MDV or TAK) or up to two lines of chemotherapy; all prior therapy except Lupron must have been discontinued for more than weeks before enrollment Willing to take abiraterone acetate on an empty stomach; no food should be consumed at least two hours before and or at least one hour after the dose abiraterone acetate is taken No prior exposure to abiraterone acetate or other specific CYP- inhibitors