Study of CAR-BCMA, a Chimeric Antigen Receptor T Cell (CAR-T) Therapy Directed Against BCMA in Subjects With Multiple Myeloma

Inclusion Criteria: 1. Bone marrow plasma cells must be at least 10% of total bone marrow cells based on a bone marrow biopsy/aspiration performed within 30 days of the start of protocol treatment. 2. Documented diagnosis of multiple myeloma according to IMWG diagnostic criteria. 3. Subjects must have measurable MM as defined by at least one of the criteria below. One or more of these abnormalities defines measurable disease 1. Serum M-protein equal or greater than 0.4 g/dl (10 g/l). 2. Urine M-protein equal or greater than 200 mg/24 h. 3. Serum free light chain (FLC) assay: involved FLC level greater or equal to10 mg/dl (100 mg/l) provided serum FLC ratio is abnormal. 4. A biopsy-proven plasmacytoma 4. Patients must have received at least 3 prior treatment regimens for multiple myeloma. 5. Greater than or equal to 18 years of age. 6. Able to understand and sign the Informed Consent Document. 7. Clinical performance status of ECOG 0-2 8. Subjects of both genders must be willing to practice birth control from the time of enrollment on this study and for four months after receiving the preparative regimen. 9. Women of child bearing potential must have a negative pregnancy test because of the potentially dangerous effects of the preparative chemotherapy on the fetus. 10. Seronegative for HIV- 1, 2 antibody. 11. Seronegative for hepatitis B surface antigen (HBsAg) or HBsAg positive with negative PCR for HBV nucleotides in blood. (Treatment to prevent HBV reactivation is standard in any case of seropositivity for HBV). 12. Seronegative for hepatitis C antibody. If hepatitis C antibody test is positive, then subjects must be tested for the presence of antigen by RT-PCR and be HCV RNA negative. 13. Syphilis negative. 14. Absolute neutrophil count greater than or equal to 500/mm3 without the support of filgrastim or other growth factors. 15. Platelet count greater than or equal to 30,000/mm3 without transfusion support 16. Hemoglobin greater than 8.0 g/dl. 17. Less than 5% plasma cells in the peripheral blood leukocytes 18. At least 14 days must have elapsed since any prior systemic therapy at the time the subject starts the cyclophosphamide and fludarabine conditioning regimen, and subjects' toxicities must have recovered to a grade 1 or less (except for toxicities such as alopecia or vitiligo). 19. Systemic anti-myeloma therapy including systemic corticosteroid therapy of greater than 5 mg/day of prednisone or equivalent dose of another corticosteroid are not allowed within 2 weeks prior to the required leukapheresis, within 2 weeks prior to CAR T-cell infusion, and for 30 days after the CAR T cell infusion, unless required for treatment of toxicity or other medical need. 20. Cardiac ejection fraction greater than or equal to 45% by echocardiography within 6 weeks of the start of the treatment protocol. Exclusion Criteria: 1. Subjects with second malignancies in addition to multiple myeloma are not eligible if the second malignancy has required treatment within the past 3 years or is not in complete remission. There are two exceptions to this criterion: successfully treated non-metastatic basal cell or squamous cell skin carcinoma. 2. Women who are pregnant or breastfeeding because of the potentially dangerous effects of the preparative chemotherapy on the fetus or infant. 3. Active systemic infections (defined as infections causing fevers or requiring antimicrobial treatment), or other major uncontrolled medical illnesses. 4. Active HBV and HCV infection which is identified by positive PCR to viral nucleotides in blood. 5. Systemic corticosteroid steroid therapy of greater than 5 mg/day of prednisone or equivalent dose of another corticosteroid are not allowed within 2 weeks prior to either the required leukapheresis or the initiation of the conditioning chemotherapy regimen. 6. Inadequate hepatic function defined by aspartate aminotransferase (AST) and/or alanine aminotransferase (ALT) \> 2.5 x upper limit of normal (ULN) and direct bilirubin \> 2 x ULN 7. Inadequate renal function defined by serum creatinine clearance /estimated clearance of ≤ 20(ml/min). 8. History of severe immediate hypersensitivity reaction to any of the agents used in this study. 9. Subjects with CNS involvement. 10. Received an investigational intervention (including investigational vaccines) or used an invasive investigational medical device within 15 days prior to leukapheresis for CAR T-cell manufacture, or is currently enrolled in an investigational study. However, prior therapy with belantamab mafotodin can be used.