Immunotherapy With BCMA CAR-T Cells in Treating Patients With BCMA Positive Relapsed or Refractory Multiple Myeloma

This phase I trial studies the side effects and best dose of BCMA CAR-T cells in treating patients with BCMA positive multiple myeloma that has come back or does not respond to treatment. T cells are a type of white blood cell and a major component of the immune system. T-cells that have been genetically modified in the laboratory express BCMA and may kill cancer cells with the protein BCMA on their surface. Giving chemotherapy before BCMA CAR-T cells may reduce the amount of disease and to cause a low lymphocyte (white blood cell) count in the blood, which may help the infused BCMA CAR-T cells survive and expand.