High Dose Testosterone for ATM, CDK12 or CHEK2 Altered Prostate Cancers

Inclusion Criteria: * Signed informed consent form (ICF) providing agreement to adhere to the dosing schedule, report for all trial visits and authorization, use and release of health and research trial information * Histologically or cytologically confirmed adenocarcinoma of the prostate * Ongoing gonadal androgen deprivation therapy with gonadotropin-releasing hormone (GnRH) analogues, antagonists or orchiectomy. Patients who have not had an orchiectomy must be maintained on effective GnRH analogue/antagonist therapy * Castration resistant prostate cancer as defined by serum testosterone \< 50 ng/ml and one of the following: * PSA level of at least 2 ng/ml that has risen on at least 2 successive occasions at least 1 week apart. * Evaluable disease progression by modified RECIST 1.1 (Response Evaluation Criteria in Solid Tumors) * Progression of metastatic bone disease on bone scan with \> 2 new lesions * Presence of metastatic disease on bone or CT scan * Patients must have progressed on 1 next-generation AR-signaling inhibitor (e.g. abiraterone, enzalutamide, apalutamide, darolutamide, etc.). * Asymptomatic or minimal cancer related symptoms * Eastern Cooperative Oncology Group (ECOG) Performance Status of \< 2 * Presence of inactivating mutations in ATM, CDK12 or CHEK2 as determined by a CLIA level assay for DNA sequencing. Exclusion Criteria: * Currently receiving active therapy for other neoplastic disorders will not be eligible. * Histologic evidence of small cell carcinoma (morphology alone - immunohistochemical evidence of neuroendrocrine differentiation without morphologic evidence is not exclusionary) * Known parenchymal brain metastasis * Liver metastases * Active or symptomatic viral hepatitis or chronic liver disease AST or ALT \> 2.5 x ULN or total bilirubin \> ULN (unless Gilbert's syndrome is the etiology of hyperbilirubinemia). * Clinically significant heart disease as evidenced by myocardial infarction, or arterial thrombotic events in the past 6 months, severe or unstable angina, or New York Heart Association (NYHA) Class II-IV heart disease or cardiac ejection fraction measurement of \<35 % at baseline * Patients with pain attributable to their prostate cancer and requiring the use of opioids. * Tumor causing urinary outlet obstruction that requires catheterization for voiding. Patients that require catheterization to void secondary to benign strictures or other non-cancer causes will be permitted to enroll. * Presence of dementia, psychiatric illness, and/or social situations limiting compliance with study requirements or understanding and/or giving of informed consent. * Any condition(s), medical or otherwise, which, in the opinion of the investigators, would jeopardize either the patient or the integrity of the data obtained.