Additional Study Information: This research study is investigating a new treatment for cancer that uses your immune system (a type of white blood cell called T cells or T lymphocytes) to try to attack your cancerous cells. T cells fight infections, and may attack cancer cells, in some cases. Currently, your T cells may not able to attack your cancerous cells. The use of these modified T cells (called CART-PSMA cells) is experimental and this is an early research study (or clinical trial) in which the CART-PSMA-TGFDN cells are being tested in humans. An early research study means that only a few people have been treated with CART-PSMA-TGFDN modified T cells. Currently, we do not know the best and safest dose of CART-PSMA-TGFDN cells. The goal of this research study is to find a safe dose in people with advanced prostate cancer, which has spread beyond the prostate and is not responding to hormone therapies. This will be done by using different planned doses of the CART-PSMA-TGFDN cells in small groups of participants, also called a cohort, in this research study. Your study physician will be able to tell you to which cohort you may be assigned. There will be 5 cohorts in this study, and based on how the patients tolerate the infusion of CART-PSMA-TGFDN, other doses may be explored. There will be about 18 people taking part in this study.