IL-18 Armored STEAP1 CAR T Cells for the Treatment of Metastatic Castration Resistant Prostate Cancer

Inclusion Criteria: * Documented, histologically confirmed adenocarcinoma of the prostate * Measurable disease by RECIST 1.1 criteria or bone only metastases with measurable PSA (≥ 1ng/mL) * Must have mCRPC with progressive disease (PD), stable disease (SD), lack of clinical benefit or intolerance to ≥ 1 line of systemic therapy, after becoming castration resistant * Have received the following for metastatic prostate cancer: * At least two lines of Food and Drug Administration (FDA)-approved therapies with at least one being a second-generation androgen receptor signaling inhibitor. * Targeted therapies for which they are eligible in the metastatic setting unless the patient has contraindications to receiving those medications, the agents are not available to the patient or the patient declines to receive these drugs due to personal preference * 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 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 FH-STEAP1 IL-18 CAR T cell infusion * 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 * Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 * 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 at 1 second (FEVI) ≥ 50% of predicted and carbon monoxide diffusing capability (DLCO) (adjusted for lung volume) of ≥ 40% of predicted will be eligible * All 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 an echocardiogram or MUGA scan, and left ejection fraction must be ≥ 45% * Absolute neutrophil count (ANC) \> 1500 cells/ mm\^3 * Hemoglobin ≥ 9g 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 * Patients that require immediate therapy due to mass effect or spinal cord compression * Active autoimmune disease: Participants with active autoimmune disease requiring chronic immunosuppressive therapy are excluded. Case by case exemptions are possible with approval by principal investigator (PI) * Corticosteroid therapy at a dose equivalent of \> 10 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 * Uncontrolled concurrent illness: Participants may not have uncontrolled respiratory, endocrine, renal, gastrointestinal, genitourinary or systemic infection. There are exceptions to this criterion: * 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; * Patients who have recent history of cerebrovascular accident, transient ischemic attack should be cleared by the neurology service before enrolling this study * Patients who have recent history of coronary artery disease or cardiac arrhythmia should be cleared by the cardiology service before enrolling this study. Case by case exemptions are possible with approval by PI * Participants with brain metastasis * 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 \> 10 mg prednisone (or equivalent) per day, unless otherwise approved by PI * Patients with a second malignancy in addition to their prostate cancer are not eligible if the second malignancy has required systemic treatment within the past 4 years or is not in complete remission. There are exceptions to this criterion: successfully treated non-metastatic basal cell and squamous cell skin carcinoma * 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 * Participants who do not have a reasonable standard-of-care bridging therapy option available, as determined by the treating medical oncologist, to maintain disease control should clinically significant disease progression or worsening symptoms occur during the screening and T-cell manufacturing period