MCARH109 Chimeric Antigen Receptor (CAR) Modified T Cells for the Treatment of Multiple Myeloma

Inclusion Criteria: * Patients must have histologically confirmed MM by MSKCC pathologist. * Age ≥ 18 years of age * Diagnosis of relapsed or refractory multiple myeloma with at least 3 prior lines of therapy. * Refractory myeloma is defined as disease that progresses while on therapy or within 60 days after the last therapy. Relapsed myeloma id defined as previously treated myeloma with initial response and subsequent progression (per IMWG criteria) not meeting criteria for refractory disease. * At least 3 prior lines of therapy; Prior therapy should include all of the following- * A proteasome inhibitor (e.g. bortezomib, carfilzomib, ixazomib) * An immunomodulatory drug (e.g. thalidomide, lenalidomide, pomalidomide) * A CD38 monoclonal antibody (e.g. daratumumab) * High dose chemotherapy with autologous stem cell support (ASCT) Subjects who are not candidates to receive one or more of the above treatments are eligible for the trial * ECOG performance status of 0 or 1 * HGB ≥ 8 g/dl, ANC≥ 1,000/mm3, Platelet≥ 50,000/mm3 without red cell transfusion for 21 days, platelet transfusion for 7 days and or growth factor support (Neupogen or Neulasta) for at least 14 days prior to initial screening (screening A). HGB ≥ 8 g/dl, ANC≥ 1,000/mm3, Platelet≥ 20,000/mm3 prior to pre-treatment screening (screening B). Patients are allowed to receive transfusion support prior to the pre-treatment screening but no growth factor support (Neupogen or Neulasta) for 7 days prior to pre-…