Adenosine Receptor Antagonist Combination Therapy for Metastatic Castrate Resistant Prostate Cancer

General Inclusion Criteria: * Male participants; age ≥ 18 years * Metastatic castrate-resistant prostate cancer while on anti-androgen treatment with castrate levels of testosterone (≤1.7 nanomoles per liter \[nmol/L\] or 50 nanograms per deciliter \[ng/dL\]) * Measurable or non-measurable disease as per radiographic evaluation * Participants with measurable disease may require a fresh tumor biopsy at study entry * Eastern Cooperative Oncology Group (ECOG) Performance status of 0 or 1 * Life expectancy of at least 3 months * Adequate hematologic and end-organ function * Human immunodeficiency virus (HIV), Hepatitis B, and C test results negative prior to first study treatment Inclusion Criteria for Participants receiving an enzalutamide-containing treatment * Disease progression after prior treatment with abiraterone Inclusion Criteria for Participants receiving a docetaxel-containing treatment * Disease progression after prior androgen synthesis inhibitor therapy Inclusion Criteria for all other Participants * Disease progression after prior androgen synthesis inhibitor treatment and up to 2 prior lines of taxane chemotherapy General Exclusion Criteria: * Prior treatment with immune checkpoint blockade therapy * Prior anticancer treatment including approved agents, systemic radiotherapy, or investigational therapy, within 2-4 weeks prior first study treatment * Corrected QT interval (QTc) ≥480 msec using Fredericia's QT correction formula (based on an average of triplicate recordings) * Prior allogeneic stem cell or solid organ transplantation * Prior treatment with drugs that stimulate the immune system within 4 weeks prior to first study treatment * Prior treatment with drugs that suppress the immune system within 2 weeks prior to first study treatment * Received a live, attenuated vaccine within 4 weeks prior to first study treatment, or may need to receive a vaccine during study treatment * Presence of metastases in the brain or cancer spreading into the cerebrospinal fluid - CSF (leptomeningeal disease) * Prior pulmonary fibrosis, pneumonia, or pneumonitis * Cancer other than prostate within 2 years prior to study entry, except for some cancers with a low risk of spreading like non-melanoma skin * Prior treatment with an agent targeting the adenosine pathway * No oral or IV antibiotics within 2 weeks prior to first study treatment * No severe infection within 4 weeks prior to first study treatment * No clinically significant cardiac disease * Inability to swallow medications Exclusion Criteria for Participants receiving an enzalutamide-containing treatment * Prior treatment with docetaxel, cabazitaxel, or other taxane chemotherapy (prior docetaxel \[up to 6 cycles\] for hormone-sensitive prostate cancer is allowed if the last dose was at least 6 months prior to study treatment initiation) * Prior treatment with enzalutamide or similar therapy other than abiraterone * Active or history of autoimmune disease or immune deficiency * History of severe allergic reactions to antibody therapy * Concomitant use of a medication prohibited by the protocol (including certain transporter substrates as well as known strong CYP3A4 inducers and CYP3A4 inhibitors) within 4 weeks prior to and throughout study treatment Exclusion Criteria for Participants receiving a docetaxel-containing treatment * Prior treatment with docetaxel, cabazitaxel, or other taxane chemotherapy * Active or history of autoimmune disease or immune deficiency * History of severe allergic reactions to antibody therapy * Concomitant use of a medication prohibited by the protocol (including certain transporter substrates as well as known strong CYP3A4 inducers and CYP3A4 inhibitors) within 4 weeks prior to and throughout study treatment Exclusion Criteria for all other Participants * Prior treatment with docetaxel, cabazitaxel, topoisomerase 1 inhibitors, or other taxane chemotherapy * Active or history of autoimmune disease or immune deficiency * History of severe allergic reactions to antibody therapy * Concomitant use of a medication prohibited by the protocol (including certain transporter substrates as well as known strong CYP3A4 inducers and CYP3A4 inhibitors) within 4 weeks prior to and throughout study treatment