A Phase 1 Study of BPX-601 CAR T-Cell Therapy in Adult Participants With Prostate Cancer That Has Returned, is Resistant to Treatment and Has Spread

This study will test a study drug called BPX-601, a CAR-T cell product manufactured from the patient's own T-cells, to see if it can help treat advanced prostate cancer. BPX-601 is a drug that is only used in clinical studies. The study is looking at: * What side effects BPX-601 might cause * What is the best dose of BPX-601 * How well BPX-601 may work to destroy prostate cancer

Key Inclusion Criteria: 1. Histologically or cytologically confirmed diagnosis of hormone-refractory adenocarcinoma of the prostate without pure small cell carcinoma 2. Metastatic, Castration-Resistant Prostate Cancer (mCRPC) with PSA value at screening ≥4 ng/mL that has progressed within 6 months prior to screening, as defined in the protocol 3. Has received ≥2 lines prior systemic therapy approved in the metastatic and/or castration-resistant setting \[in addition to Androgen Deprivation Therapy (ADT)\] including at least 1 second-generation anti-androgen therapy (eg, abiraterone, enzalutamide, apalutamide, or darolutamide) 4. Has had either orchiectomy OR is on Luteinizing Hormone-Releasing Hormone (LHRH) agonist or antagonist therapy with serum testosterone \5 × ULN, if liver metastases, and/or total bilirubin \>1.5 × ULN, as described in the protocol 5. Inadequate bone marrow function defined by Absolute Neutrophil Count (ANC) \