TmPSMA-02 in mCRPC

Inclusion Criteria: 1. Signed, written informed consent 2. Adult participants ≥ 18 years of age 3. Metastatic castrate-resistant prostate cancer (mCRPC) 4. Castrate levels of testosterone (\<50 ng/dL) with/without the use of androgen-deprivation therapy 5. Received at least one prior standard therapy for systemic treatment in the mCRPC setting, including at least one second generation androgen receptor signaling inhibitor (e.g., enzalutamine, apalutamide, darolutamide, or abiraterone) or a taxane-based regimen (e.g., docetaxel, cabazitaxel, etc). 6. Adequate organ function within 4 weeks of eligibility confirmation by a physician-investigator defined as: 1. Serum creatinine ≤ 1.5 mg/dl or creatinine clearance ≥ 50 cc/min per the Cockcroft-Gault Equation; Patient must not be on dialysis 2. ALT/AST ≤ 3 x ULN 3. Serum total bilirubin ≤ 1.5 mg/dL, unless the subject has Gilbert's syndrome (if so, serum total bilirubin must be ≤3.0 mg/dL) 4. Left Ventricle Ejection Fraction (LVEF) ≥ 45% confirmed by ECHO 5. Must have a minimum level of pulmonary reserve defined as ≤ Grade 1 dyspnea and pulse oxygen \> 92% on room air 7. Patients must have adequate hematologic reserve within 4 weeks of eligibility confirmation by a physician-investigator and must not be dependent on transfusions to maintain these hematologic parameters. Adequate hematologic reserve is defined as: 1. Hemoglobin ≥ 8 g/dL 2. Absolute neutrophil count ≥ 1000/μL 3. Platelet count ≥ 75,000/μL 8. ECOG Performance Status that is either 0 or 1. 9. Patients who have not undergone bilateral orchiectomy must be able to continue GnRH therapy during the study. 10. Participants of reproductive potential must agree to use acceptable birth control methods, as described in the protocol. Exclusion Criteria: 1. Active hepatitis B or hepatitis C infection 2. Any other active, uncontrolled infection 3. Class III/IV cardiovascular disability according to the New York Heart Association Classification. 4. Severe, active co-morbidity that in the opinion of the physician-investigator would preclude participation in the study. 5. Active invasive cancer, other than the proposed cancer included in the study, within 2 years prior to eligibility confirmation by a physician-investigator. \[Note: non-invasive cancers treated with curative intent (e.g., non-melanoma skin cancer) may still be eligible\]. 6. Patients requiring chronic treatment systemic steroids or immunosuppressant medications. Low-dose physiologic replacement therapy with corticosteroids equivalent to prednisone 10 mg/day or lower, topical steroids and inhaled steroids are acceptable. For additional details regarding use of steroid and immunosuppressant medications, please see Section 5.6. 7. Prior treatment with autologous T-cell therapy, with the exception of Sipuleucel-T. 8. Prior allogeneic stem cell transplant. 9. Active autoimmune disease requiring systemic immunosuppressive treatment equivalent to ≥ 10mg of prednisone. Patients with autoimmune neurologic diseases (such as MS) will be excluded. 10. History of allergy or hypersensitivity to study product excipients (human serum albumin, DMSO, and Dextran 40).