A Study of TmPSMA-02 Chimeric Antigen Receptor (CAR) T-cells in Patients With Metastatic Castration Resistant Prostate Cancer (mCRPC)

Inclusion Criteria: * Adults at least 18 years of age. * A confirmed histologic diagnosis of prostate cancer. * Castrate levels of testosterone (\< 50 ng/dL). * Measurable disease (radiographic or Prostate Specific Antigen \[PSA\]) per PCWG3 criteria (see Appendix 3) * Received at least 2 prior lines of systemic therapy for prostate cancer, including at least one second generation androgen receptor inhibitor (e.g., enzalutamide or apalutamide) or CYP17α inhibitor (e.g., abiraterone/ prednisone) and a taxane based regimen (e.g., docetaxel, cabazitaxel, etc). At least one line of prior therapy must be in the mCRPC setting. Note: Androgen deprivation therapy (ADT) with gonadotropin- releasing hormone (GnRH) agonist/antagonist does not count as a line of therapy nor does a first-generation nonsteroidal antiandrogen (e.g., bicalutamide, flutamide, etc.). * Adequate vital organ function as defined by: (A) Estimated glomerular filtration rate (eGFR) eGFR ≥ 50 mL/min by Modification of Diet in Renal Disease criteria, (B) Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤ 2.5 x the upper limit of normal (ULN); patients with hepatic metastases ALT and AST ≤ 3.0 ULN. (C) Serum total bilirubin \< 1.5 × ULN unless patient has known Gilbert's; if so, then serum bilirubin ≤ 3 mg/dL, or (D) Left ventricular ejection fraction ≥ 45%. * Patients must have adequate hematologic reserve and must not be dependent on transfusions to maintain these hematologic parameters. Adequate hematologic reserve is defined as: (A) Hemoglobin ≥ 8 g/dL, (B) absolute neutrophil count ≥ 1000/ μL, or (C) Platelet count ≥ 75,000/μL. * Patients who have not undergone bilateral orchiectomy must be able to continue 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 to the baseline. Exceptions include non-clinically significant toxicities as a result of previous therapy (e.g., alopecia, hormonal changes, weight loss, etc). * Patients of reproductive potential agree to use protocol-specified highly effective contraceptive methods Exclusion Criteria: * Active invasive cancer, other than the proposed cancer included in the study, within 2 years prior to screening. \[Note: non-invasive cancers treated with curative intent (e.g., non-melanoma skin cancer may still be eligible\], unless treated with curative intent, i.e., non-melanoma skin cancer. * Prior treatment with autologous T-cell therapy. Note: Prior treatment with Sipuleucel-T is allowed. * Patients who require chronic treatment with systemic corticosteroids (defined as a dose greater than the equivalent of prednisone 10 mg/day). Low-dose physiologic replacement therapy with corticosteroids equivalent to prednisone 10 mg/day or lower, topical steroids and inhaled steroids are acceptable. * Prior allogeneic stem cell transplant. * Active autoimmune disease (including, but not limited to, connective tissue disease, uveitis, sarcoidosis, inflammatory bowel disease or multiple sclerosis) or a history of severe autoimmune disease requiring prolonged immunosuppressive therapy. Patients should have stopped any immunosuppressive therapy within 6 weeks prior to Screening. * Current infection with human immunodeficiency virus (HIV), hepatitis C virus (HCV), or hepatitis B virus (HBV). Viral testing at Screening is required in all patients to rule out subclinical infections. Patients who are hepatitis B core antibody positive and hepatitis B surface antigen negative should have quantitative viral load measured. If viral load is undetectable, the patient may enroll and be monitored as per ASCO Guidelines. * Seizure disorder requiring anti-epileptic medications. * History of severe infusion reaction to monoclonal antibodies or biological therapies, or to study product excipients (e.g., human serum albumin, dimethyl sulfoxide \[DMSO\], dextran 40) that would preclude the patient safely receiving TmPSMA-02. * History of or known predisposition to hemophagocytosis lymphohistiocytosis (HLH) or macrophage activation syndrome (MAS) * Any active infection currently being treated with antibiotics, anti-virals or anti-fungal. Prophylactic anti-microbials are not exclusionary. * Active or recent (within the past 6 months prior to leukapheresis) cardiovascular disease, defined as (1) New York Heart Association Class III or IV heart failure, (2) unstable angina or (3) a history of recent (within 6 months) myocardial infarction or sustained (\> 30 second) ventricular tachyarrhythmias, (4) cerebrovascular accident. * Active or uncontrolled medical or psychiatric condition that would preclude participation in the opinion of the Sponsor, Principal Investigator (PI) and/or their designee. * Have inadequate venous access for or contraindications for the leukapheresis procedure. Central venous access is acceptable.