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

Inclusion Criteria: * Documented informed consent of the participant and/or legally authorized representative. * Assent, when appropriate, will be obtained per institutional guidelines. * Karnofsky Performance Status (KPS) of \>= 70%. * Life expectancy \>= 16 weeks. * Participant must have a confirmed diagnosis of active MM as defined by the International Myeloma Working Group (IMWG) criteria. * Participant must have a confirmed CS1+ MM as evaluated by City of Hope (COH) Pathology Core. * Participant must have measurable disease defined as meeting at least one of the criteria below: * Serum M-protein \>= 0.5 g/dL. * Urine M-protein \>= 200 mg/24 hour. * Involved serum free light chain (sFLC) level \>= 10 mg/dL with abnormal kappa/lambda ratio. * Measurable biopsy-proven plasmacytomas (\>= 1 lesion that has a single diameter \>= 2 cm) * Bone marrow plasma cells \>= 30%. * Participant must have relapsed or refractory disease after all 3 prior treatment regimens with the following requirements: * Participant must have received prior treatment with an immunomodulatory agent. * Participant must have received prior treatment with a proteasome inhibitor. * Participant must have received prior treatment with an anti-CD38 antibody. * Participants must be refractory to last line of therapy prior to study enrollment (refractory myeloma is defined as disease that is nonresponsive, progression on treatment, or shows progression within 60 days after the last prior l…