Previous chemotherapy with at least cycles of docetaxel for hormone-sensitive metastatic prostate cancer Prior docetaxel for hormone-sensitive prostate cancer is permitted if =< doses were given in conjunction with first-line androgen deprivation therapy and > months since last dose of docetaxel Previous treatment with docetaxel for metastatic prostate cancer mCRPC EXPANSION COHORT: Patients must have received prior treatment with enzalutamide and/or abiraterone with the exception of patients who were treated with docetaxel and androgen deprivation therapy for metastatic castrate-sensitive prostate cancer and progressed on docetaxel treatment or who progress within one month of the last docetaxel dose mCRPC EXPANSION COHORT: Patients who were treated for metastatic castrate-sensitive prostate cancer with docetaxel and androgen deprivation therapy who progress on docetaxel treatment or who progress within one month of the last docetaxel dose are eligible PHASE II STUDY METASTATIC CASTRATE-RESISTANT PROSTATE CANCER COHORT ELIGIBILITY CRITERIA (MEDI+O ONLY):\r\nPatients must have received prior treatment with enzalutamide and/or abiraterone with the exception of patients who were treated with docetaxel and androgen deprivation therapy for metastatic castrate-sensitive prostate cancer and progressed on docetaxel treatment or who progress within one month of the last docetaxel dose PHASE II STUDY METASTATIC CASTRATE-RESISTANT PROSTATE CANCER COHORT ELIGIBILITY CRITERIA (MEDI+O ONLY):\r\nPatients who were treated for metastatic castrate-sensitive prostate cancer with docetaxel and androgen deprivation therapy who progress on docetaxel treatment or who progress within one month of the last docetaxel dose are eligible Prior docetaxel for hormone-sensitive prostate cancer is permitted if =< doses were given in conjunction with first-line androgen deprivation therapy and > months since last dose of docetaxel No prior chemotherapy for the treatment of mCRPC; patients may have received docetaxel for the treatment of hormone-sensitive prostate cancer Patients who are deemed to have high-risk or extensive metastatic, hormone sensitive prostate cancer (mHSPC) per clinical judgment of the treating physician are eligible for enrollment if they are unsuitable candidates for docetaxel or if they have declined docetaxel therapy Prior chemotherapy (for example, docetaxel, cabazitaxel) for treatment of CRPC, except when docetaxel has been given for hormone-sensitive prostate cancer For Cohort B: Has received prior treatment with docetaxel or another chemotherapy agent for metastatic prostate cancer For Cohort C: Has received prior chemotherapy for mCRPC. Prior docetaxel for metastatic hormone-sensitive prostate cancer is allowed if ? weeks elapsed from last dose of docetaxel Prior cytotoxic chemotherapy for prostate cancer, but up to cycles of docetaxel chemotherapy for metastatic disease is permitted. The subject has had treatment with docetaxel for the treatment of metastatic castrate-sensitive prostate cancer within months before the first dose of study treatment The subject has had progression of prostate cancer during cycles of prior docetaxel treatment for castrate sensitive disease Prior docetaxel or other chemotherapy for mCRPC; patients who have received docetaxel for metastatic hormone-sensitive prostate cancer are eligible Patients who have received docetaxel plus anti-androgen therapy (ADT) for metastatic castrate sensitive prostate cancer are eligible for the study; (patients may enroll as long as they did not have progressive disease while on docetaxel and are months removed from treatment, with all treatment related toxicities resolving to at least grade ) Have had treatment with docetaxel for the treatment of metastatic castrate-sensitive prostate cancer within months before the first dose of study enrollment Have had progression of prostate cancer on prior docetaxel treatment for castrate sensitive disease