SPECTRA: Supraphysiological Androgen to Enhance Treatment Activity
This phase II trial studies how well giving testosterone at levels higher than normally found in the body (supraphysiological) works to enhance chemotherapy treatment, and Lutetium 177Lu-prostate specific-membrane antigen (PSMA)-617 (LuPSMA) in patients with prostate cancer that has progressed despite being previously treated with androgen therapies and has spread from where it first started (prostate) to other places in the body (metastatic castration-resistant prostate cancer). In patients that have developed progressive cancer in spite of standard hormonal treatment, administering supraphysiological testosterone may result in regression of tumors by causing deoxyribonucleic acid (DNA) damage in tumor cells that have adapted to low testosterone conditions. Carboplatin is in a class of medications known as platinum-containing compounds. Carboplatin works by killing, stopping or slowing the growth of tumor cells. Etoposide is in a class of medications known as podophyllotoxin derivatives. It blocks a certain enzyme needed for cell division and DNA repair and may kill tumor cells. Radioactive drugs, such as LuPSMA, may carry radiation directly to tumor cells and not harm normal cells. Giving supraphysiological levels of testosterone and carboplatin or etoposide or LuPSMA together may be an effective treatment for metastatic castration-resistant prostate cancer.
• Must be willing to provide informed consent prior to any study specific procedures
• Age \>= 18 years
• Documented histologically confirmed adenocarcinoma of the prostate
• Patient must have evidence of castration resistant prostate cancer as evidenced by PSA progression (per Prostate Cancer Working Group 3 \[PCWG3\] criteria) and a castrate serum testosterone level (i.e., =\< 50 mg/dL)
• PSA must be at least 2 ng/ml and rising on two successive measurements at least two weeks apart
• Patients must have progressed on at least one prior next-generation androgen receptor-signalling inhibitor (e.g., abiraterone, enzalutamide, etc.). There must be at least a 2-week washout period after stopping the most recent approved therapy for metastatic castration-resistant prostate cancer (mCRPC) (e.g., abiraterone, enzalutamide, Ra-223, sipuleucel-t) prior to cycle 1, day 1. If applicable, patients should be weaned off steroids at least 1 week prior to starting treatment
• Subjects enrolling to Cohort 3 must demonstrate evidence of PSMA expression on 68Ga-PSMA-11 PET as defined in the VISION trial
• No prior chemotherapy for the treatment of mCRPC. Patients may have received docetaxel for the treatment of hormone-sensitive prostate cancer
• Prior treatment with non-chemotherapy investigational agents is permitted. There must be at least a 2-week washout period after stopping any investigational cancer agent prior to cycle 1, day 1
• Hemoglobin \>= 9 g/dL with no blood transfusion in the past 28 days (within 30 days prior to administration of study treatment)
• Absolute neutrophil count (ANC) \>= 1.5 x 10\^9/L (within 30 days prior to administration of study treatment)
• Platelet count \>= 100 x 10\^9/L (within 30 days prior to administration of study treatment)
• Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN) (within 30 days prior to administration of study treatment)
• Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) / alanine aminotransferase (ALT) (serum glutamic pyruvate transaminase \[SGPT\]) =\< 2.5 x institutional upper limit of normal unless liver metastases are present in which case they must be =\< 5x ULN (within 30 days prior to administration of study treatment)
• Patients must have creatinine clearance estimated using the Cockcroft-Gault equation or based on 24 hour urine test of \>= 51 mL/min (within 30 days prior to administration of study treatment)
• Eastern Cooperative Oncology Group (ECOG) performance status =\< 2
• Patients must have a life expectancy \>= 16 weeks
• Patient is willing and able to comply with the protocol for the duration of the study including undergoing treatment and scheduled visits and examinations
• At least one lesion (measurable and/or non-measurable) that can be accurately assessed at baseline by CT, positron emission tomography (PET), magnetic resonance imaging (MRI) and/or bone scan and is suitable for repeated assessment
• Must be willing to undergo metastatic biopsy and have a lesion amenable for biopsy
• Male patients and their partners, who are sexually active and of childbearing potential, must agree to the use of two highly effective forms of contraception in combination, throughout the period of taking study treatment and for 6 months after last dose of study drug(s) to prevent pregnancy in a partner