Inclusion Criteria:

          -  Confirmed histologic diagnosis of prostate cancer and have mCRPC, with castrate levels
             of testosterone (<50 ng/mL)

          -  PSA measurable disease per Prostate Working Group 3 (PCWG3) criteria

          -  Prior therapies defined as at least 2 prior lines of systemic therapy for prostate
             cancer, including at least one second generation androgen receptor inhibitor and/or
             CYP17α inhibitor. At least one line of prior therapy must be in the mCRPC setting

          -  Estimated estimated glomerular filtration rate ≥ 60 mL/min by Modification of Diet in
             Renal Disease criteria

          -  Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤ 2.5x the upper
             limit of normal (ULN); patients with hepatic metastases ALT and AST ≤ 3.0 x ULN

          -  Serum total bilirubin < 1.5 mg/dL unless patient has known Gilbert's Syndrome, then
             serum bilirubin ≤3 mg/dL

          -  Serum albumin ≥ 3.0 g/dL

          -  Left ventricular ejection fraction (LVEF) ≥ 50%. LVEF assessment must have been
             performed within 8 weeks of enrollment

          -  Hemoglobin ≥ 8 g/dL

          -  Absolute neutrophil count ≥ 1000/μL

          -  Platelet count ≥ 75,000/μL

          -  Patients who have not undergone bilateral orchiectomy must be able to continue
             gonadotropin-releasing hormone (GnRH) therapy during the study

          -  Eastern Cooperative Oncology Group (ECOG) score of 0 or 1

          -  Toxicities from any previous therapy must have recovered to Grade 1 or baseline

          -  Patients of reproductive potential agree to use of approved highly effective
             contraceptive methods

        Exclusion Criteria:

          -  Active invasive cancer, other than the proposed cancer included in the study, within 2
             years prior to screening, unless treated with curative intent

          -  Current treatment with systemic corticosteroids (defined as a dose greater than the
             equivalent of prednisone 10 mg/day)

          -  Active autoimmune disease (including connective tissue disease, uveitis, sarcoidosis,
             inflammatory bowel disease or multiple sclerosis) or a history of severe autoimmune
             disease requiring prolonged immunosuppressive therapy (any immunosuppressive therapy
             within 6 weeks prior to screening visit)

          -  Current human immunodeficiency virus (HIV), hepatitis C virus, hepatitis B virus
             infections; Patients who are hepatitis B core antigen positive, hepatitis B surface
             antigen negative, should have a quantitative viral load measured; If viral load is
             undetectable, the patient will not be excluded if hey are able to be treated with
             anti-viral medication for at least 7 days prior to lymphodepletion until at least 6
             months after infusion with viral load and ALT monitoring

          -  Active or uncontrolled medical or psychological condition that would preclude
             participation

          -  History of seizure disorder

          -  Prior allogeneic stem cell transplant

          -  Central nervous system malignancy

          -  History of severe infusion reaction to monoclonal antibodies or biological therapies,
             or to study product excipients that would preclude the patient safely receiving
             CART-PSMA-TGFβRDN cells

          -  History of being previously treated with a J591 antibody-based therapy

          -  Ferritin levels ≥ 4x the upper limit of normal prior to apheresis or prior to the
             start of lymphodepleting chemotherapy

          -  Active or recent (within the past 6 months prior to apheresis or lymphodepletion)
             cardiovascular disease, defined as (1) New York Heart Association Class III or IV
             heart failure, (2) unstable angina, (3) a history of recent (within 6 months)
             myocardial infarction or sustained (> 30 second) ventricular tachyarrhythmias, or (4)
             cerebrovascular accident

          -  Any active infection currently being treated or any infection within the last 6 weeks
             that required 7 days or more of IV antibiotics or any active infection within the last
             4 weeks that requires use of oral antibiotics. Patients may be eligible once these
             timeframes elapse and with evidence that the infection has completely resolved

          -  Have inadequate venous access for or contraindications for the apheresis procedure

          -  Must agree not to participate in a conception process or must agree to a highly
             effective method of contraception