Cell Therapy (STEAP1 CART) With Enzalutamide for the Treatment of Patients With Metastatic Castration-Resistant Prostate Cancer

Inclusion Criteria: * Tissue confirmation of prostate adenocarcinoma * Measurable disease by RECIST 1.1 criteria or bone only metastases with measurable PSA ( ≥ 1 ng/mL) * Must have progressed (at least 2 rising PSA levels with at least a 1-week interval and a minimum PSA of 1.0 ng/mL, progression per RECIST 1.1, or 2 or more new bone lesions by bone scan), after becoming castration-resistant * Have received the following for metastatic prostate cancer: * At least two lines of treatment * At least two Food and Drug Administration (FDA)-approved therapies with at least one being a second generation androgen receptor signaling inhibitor (e.g., abiraterone, darolutamide, apalutamide, or enzalutamide) * All available targeted therapies for which they are eligible in the metastatic setting (e.g., PARP inhibitors for BRCA 1/2 and immune checkpoint inhibitor for MSI-H or TMB-H ≥ 10 mut/Mb) * Castrate levels of testosterone (\< 50 ng/dL) with or without the use of androgen deprivation therapy * 18 years or older at the time of enrollment * Capable of understanding and providing a written informed consent * Fertile male participants and their female partners must be willing to use an effective contraceptive method before, during, and for at least 4 months after the STEAP1 CART cell infusion * Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 * Participants will be permitted to receive radiation therapy for palliative purposes throughout the study period, except during the 2-week period prior to undergoing leukapheresis * Serum creatinine =\< 1.5 x upper limit of normal (ULN) or estimated creatinine clearance \> 50 mL/min as calculated using the Cockcroft-Gault formula and not dialysis dependent * Total bilirubin ≤ 1.5 x ULN. Participants with suspected Gilbert syndrome may be included if Total bilirubin (Bili) \> 3 mg/dL but no other evidence of hepatic dysfunction * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) \< 5 x ULN * ≤ grade 1 dyspnea and oxygen saturation (SaO2) ≥ 92% on ambient air * If pulmonary function tests (PFTs) are performed based on the clinical judgement of the treating physician, participants with forced expiratory volume in 1 second (FEVI) \>= 50% of predicted and diffusion capacity of the lung for carbon monoxide (DLCO) (corrected) of \>= 40% of predicted will be eligible * Participants \>= 60 years of age are required to have left ventricular ejection fraction (LVEF) evaluation performed within 1 year prior to lymphodepletion chemotherapy. LVEF may be established with echocardiogram or MUGA scan, and left ejection fraction must be \>= 35%. Cardiac evaluation for other participants is at the discretion of the treating physician * Absolute neutrophil count (ANC) \> 1500 cells/ mm\^3 * Hemoglobin \> 9 g/dL * Platelets \> 100,000 per mm\^3 Exclusion Criteria: * Expecting to conceive or father children for the duration of the trial through 4 months after T cell infusion * Active autoimmune disease: Participants with active autoimmune disease requiring immunosuppressive therapy are excluded. Case by case exemptions are possible with approval by principal investigator (PI) * Corticosteroid therapy at a dose equivalent of \>15 mg of prednisone per day (or equivalent). Pulsed corticosteroid use for disease control is acceptable * Concurrent use of other investigational anti-cancer agents except for androgen deprivation therapy * Active uncontrolled infection: human immunodeficiency virus (HIV) positive participants on highly active antiretroviral therapy (HAART) with a CD4 count \> 500 cells/mm\^3 are considered controlled, as are individuals with a history of hepatitis C who have successfully completed antiviral therapy with an undetectable viral load, and those with hepatitis B who have hepatitis well controlled on medication * Uncontrolled concurrent illness: Participants may not have uncontrolled or concurrent illness including, but not limited to, symptomatic congestive heart failure, unstable angina pectoris, or cardiac arrhythmia that would limit compliance with study requirements * Untreated brain metastases: Participants with small asymptomatic brain metastases ( \< 1 cm) or those with brain metastases previously treated and controlled with surgery or radiotherapy will be considered for inclusion at discretion of principal investigator, so long as all other eligibility criteria are met * Active treatment for prior immune related adverse event to any immunotherapy: Participants receiving ongoing treatment for prior serious immune-related adverse events are excluded, with exception of hormone supplementation or corticosteroid therapy at equivalent of \> 15 mg prednisone (or equivalent) per day, unless otherwise approved by PI * Significant underlying neurologic disease: Study participants must not have significant active underlying neurologic disease, unless approved by PI. Peripheral neuropathy related to diabetes or prior chemotherapy is acceptable * Other medical, social, or psychiatric factor that interferes with medical appropriateness and/or ability to comply with study, as determined by the PI * Known allergic reactions to any of the components of study treatments