Patients must have castrate serum level of testosterone of < 50 ng/dL (< 1.73 nmol/L) For patients with non-castrate levels of circulating androgen levels (testosterone >= 50 g/dl)\r\n* PSA levels should be increasing on at least two occasions >= 1 week apart\r\n* Patients should not be considered candidates for radiation therapy Evidence of castrate testosterone level < 50 ng/dL (or surgical castration) Patients must have histologically documented adenocarcinoma of the prostate with progressive systemic (clinically metastatic disease documented on bone, CT, or magnetic resonance imaging (MRI) scan) disease despite castrate levels of testosterone (<50 ng/dL) due to orchiectomy or luteinizing hormone-releasing hormone (LHRH) agonist. Castrate levels of testosterone must be maintained. Progressive metastatic prostate cancer despite castrate levels of testosterone (< 50 ng/dL) castrate serum level of testosterone of ? 50 ng/dL (? 1.73 mmol/L) Non-castrate testosterone level, > 50 ng/dl, at study enrollment Documented castrate level of serum testosterone (< 50 ng/dl) Non-castrate level of testosterone: >= 50 ng/dL (prior androgen deprivation therapy [ADT] allowed; must be >= 6 months since last dose of ADT) Patients must have castrate levels of testosterone (< 50 ng/dL [1.74 nmol/L]). Castrate testosterone level (< 50ng/dl or 1.7nmol /L); (patients with a malignancy other than prostate cancer are excluded from this criterion) Castrate testosterone level (< 50ng/dl or 1.7nmol /L) Patient must have evidence of castrate resistant prostate cancer as evidenced by a confirmed rising PSA (per PCWG3 criteria) and a castrate serum testosterone level (i.e. =< 50 mg/dL) Progression of metastatic prostate cancer in the setting of castrate levels of testosterone or history of bilateral orchiectomy at study entry Castrate testosterone level (< 50ng/dl or 1.7nmol /L) Metastatic castration resistant prostate cancer with castrate-level testosterone (< 50 ng/dL)\r\n* Subjects must maintain a castrate-level testosterone during the study Tumor progression while on hormone therapy with castrate levels serum testosterone (=< 1.7 nmol/L or 50 ng/dL) defined by prostate-specific antigen (PSA) and/or radiographic criteria according to the Prostate Cancer Working Group 3 (PCWG3). Castrate levels of testosterone must be maintained by surgical or medical means throughout the conduct of the study. Castrate levels of serum total testosterone (=< 50 ng/dl) OR ongoing documented androgen deprivation therapy (ADT) unless pure small cell prostate cancer is present Men with metastatic castrate-resistant prostate cancer (prostate cancer progressing despite castrate levels of testosterone [< 50 ng/dL]), using standard measures of progression defined by Prostate Cancer Working Group 2 (PCWG2) Subjects must be castration resistant with evidence of progressive prostate cancer despite castrate levels of testosterone (=< 50 ng/dL) according to the PCWG3 criteria Castrate testosterone level (< 50 ng/dl or 1.7 nmol/L) Progression of metastatic prostate cancer in the setting of castrate levels of testosterone or history of bilateral orchiectomy at study entry mCRPC EXPANSION COHORT: Patients must have castrate levels of testosterone (< 50 ng/dl [1.74 nmol/l]) PHASE II STUDY METASTATIC CASTRATE-RESISTANT PROSTATE CANCER COHORT 4 ELIGIBILITY CRITERIA (MEDI+O ONLY):\r\nPatients must have castrate levels of testosterone (< 50 ng/dl [1.74 nmol/l]) Documented castrate level of serum testosterone (< 50 ng/dl) Castrate level of testosterone (< 50 ng/dL) Patient must have evidence of castration resistant prostate cancer as evidenced by PSA progression (per Prostate Cancer Working Group 3 [PCWG3] criteria) and a castrate serum testosterone level (i.e., ? 50 mg/dL) Known castrate-resistant disease with serum testosterone level less than or equal to (= 150 ng/dL) Maintain castrate levels of testosterone within 4 weeks prior to randomization and throughout the study Participants must have progressive disease despite ongoing androgen deprivation therapy (ADT) and castrate levels of testosterone, defined as castration resistant prostate cancer (CRPC) Castrate testosterone level (< 50 ng/dl or 1.7 nmol/L) Castrate serum testosterone level, =< 1.73 nmol/L (50 ng/dL), at the screening visit For cohorts 1, 2, and 4 only: non-castrate testosterone level (> 100 ng/dL) Castrate levels of serum testosterone of less than or equal to 50 ng/dL Castrate serum testosterone (< 50 ng/dL) The subject must currently have castration resistant prostate cancer defined as 2 serial rising prostate-specific antigens (PSAs) with a castrate level of testosterone (< 50 ng/dL) Castrate levels of serum testosterone (=< 50 ng/dL or 1.0 mmol/L) confirmed within two weeks prior to day 1 of treatment; testosterone levels will not be required for patients who have had bilateral orchiectomy Patient must have evidence of castrate resistant prostate cancer as evidenced by a confirmed rising PSA (per Prostate Cancer Working Group 2 [PCWG2] criteria) and a castrate serum testosterone level (i.e. =< 50 mg/dL) Castrate resistant progression of prostate carcinoma, as shown by:\r\n* Serum testosterone level =< 30 ng/dL or prior bilateral orchiectomy; treatment to remain castrate levels of testosterone should continue, and\r\n* Either symptomatic progression, or, if patient is asymptomatic then a rising serum PSA in two occasions at least 1 week apart, with minimum pre-treatment serum PSA of 5 ng/dL Patient must have evidence of castration resistant prostate cancer as evidenced by a confirmed rising PSA (per Prostate Cancer Working Group 2 [PCWG2] criteria) and a castrate serum testosterone level (i.e. =< 50 mg/dL) Testosterone level < 50 ng/dL; patients receiving luteinizing hormone-releasing hormone (LHRH) agonists or antagonists must be continued to maintain castrate levels of testosterone while on study Patients with pure small cell neuroendocrine carcinoma on histology are not required to have received prior androgen deprivation therapy (ADT) or castrate levels of testosterone, but their testosterone state should be maintained for the duration of the study. Other patients are required to have surgical or ongoing chemical castration, with baseline testosterone level <50ng/dL. Castrate-resistant prostate cancer (CRPC) with bone metastasis: --Progressive Disease in the setting of castrate level of testosterone Castrate serum testosterone level: =< 50 ng/dL (=< 1.7 nmol/L) Histologically documented adenocarcinoma of the prostate with systemic bone or node metastatic disease despite castrate levels of testosterone (< 50 ng/dL) due to orchiectomy or luteinizing hormone-releasing hormone (LHRH) agonist; castrate levels of testosterone must be maintained while on study; men can be enrolled prior to starting abiraterone and/or enzalutamide OR already be receiving treatment with abiraterone and/or enzalutamide Metastatic disease that has progressed despite castrate levels of testosterone (surgically or medically castrated, with testosterone levels of < 50 ng/dL) SUB-STUDY III: Castrate-levels of testosterone (total testosterone < 50 ng/dL) Multifocal metastatic disease in either castrate sensitive or castrate resistant patients At the time of enrollment, patients must demonstrate evidence of castration-resistant prostate cancer with a documented castrate level of serum total testosterone (< 50 ng/dL) while on continuous androgen deprivation therapy Must continue ongoing androgen deprivation therapy with castrate levels of serum testosterone <50 nanogram/deciliter (ng/dL)