CS1-CAR T Therapy Following Chemotherapy in Treating Patients With Relapsed or Refractory CS1 Positive Multiple Myeloma

PRIMARY OBJECTIVE: I. To evaluate the safety and tolerability of intravenous (i.v.) delivered autologous CS1-CAR T cells for research participants with CS1+ recurrent/refractory multiple myeloma (MM). SECONDARY OBJECTIVES: I. Evaluate the response rates at days 28, 100, and 180 post CAR T cell infusion. II. Measure the persistence of CS1-CAR T cells in blood and marrow. III. Measure phenotype and anti-tumor functionality of CS1-CAR T cells in marrow and blood. IV. Measure the levels of cytokines in blood and marrow, and soluble CS-1 in blood post infusion as a surrogate indicator of CAR T cell activity. V. Evaluate CS-1 expression on MM cancer cells before, during and at progressive disease (PD) to determine antigenic loss. EXPLORATORY OBJECTIVE: I. Describe the percentage of MM cells that express CS-1 surface marker before, during and at PD. OUTLINE: This is a dose-escalation study of CS1-CAR T cells. Patients undergo leukapheresis over 2-4 hours. Beginning 3-4 weeks, patients receive cyclophosphamide intravenously (IV) on days -4 and/or -3 or fludarabine IV and cyclophosphamide IV on days -5 to -3. Patients then undergo CS1-CAR T therapy over 10-15 minutes on day 0. After completion of study treatment, patients are followed up at 1 day, at least every 2 days for up to a minimum of 14 days, weekly for 1 month, monthly for 1 year, then periodically for up to 15 years.