Bipolar Androgen Therapy to Restore Sensitivity to Androgen Deprivation Therapy for Patients With Metastatic Castration Resistant Prostate Cancer

Inclusion Criteria: * Age ≥ 18 years of age * Have an Eastern Cooperative Oncology Group (ECOG) performance status of ≤ 2 * Histologically confirmed carcinoma of the prostate * Progressing on continuous androgen ablative therapy (either surgical castration or LHRH agonist) * Documented castrate level of blood testosterone (\< 50 ng/dL) * Patients must have progressed on prior treatment with at least one Androgen Receptor Signaling Inhibitors (ARSI) (by prostate specific antigen \[PSA\] criteria or radiographically) * Have biopsiable disease (a fresh biopsy is not required at baseline if adequate archival tissue is available) * Absolute neutrophil count: ≥1,200/µL * Platelets: ≥ 100,000/µL * Total bilirubin: ≤ 1.2 x institutional upper limit of normal (ULN) * Aspartate aminotransferase (AST)(serum glutamic oxaloacetic transaminase \[SGOT\])/ Alanine aminotransferase (ALT) (serum glutamic pyruvic transaminase \[SGPT\]): ≤ 3 × institutional ULN * Creatinine clearance (CrCl) \> 50 mL/min (Cockcroft-Gault equation) * Have measurable disease per Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 criteria present * Participants of child-bearing potential must agree to use adequate contraceptive methods (e.g., hormonal or barrier method of birth control; abstinence) prior to study entry. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately * Participant must unde…