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 understand the investigational nature of this study and sign an Independent Ethics Committee/Institutional Review Board approved written informed consent form prior to receiving any study related procedure Exclusion Criteria: * Participants who have had chemotherapy or radiotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier * Participants with known brain metastases should be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events * Greater than 5 sites of visceral disease in lung or liver (nonspecific lung nodules ≤ 1 cm in diameter is permitted) * Evidence of disease in sites or extent that, in the opinion of the investigator, would put the patient at risk from therapy with testosterone (e.g., femoral metastases with concern over fracture risk, spinal metastases with concern over spinal cord compression, lymph node disease with concern for ureteral obstruction) * Active uncontrolled infection, including known history of acquired immunodeficiency syndrome (AIDS) or hepatitis B or C * Any psychological, familial, sociological, or geographical condition that could potentially interfere with compliance with the study protocol and follow-up schedule * Prior history of a thromboembolic event within the last 12 months and not currently on systemic anticoagulation * Hematocrit \> 50%, untreated severe obstructive sleep apnea, uncontrolled or poorly controlled heart failure (per Endocrine Society Clinical Practice Guidelines) * Evidence of serious and/or unstable pre-existing medical, psychiatric, or other condition (including laboratory abnormalities) that could interfere with patient safety or provision of informed consent to participate in this study * Known allergy to testosterone cypionate or any of its excipients * Unwilling or unable to follow protocol requirements * Any condition which in the Investigator's opinion deems the participant an unsuitable candidate to receive study drug