Anti-BCMA Chimeric Antigen Receptor T Cells for Relapsed or Refractory Multiple Myeloma

Eligibility for enrollment: Inclusion Criteria: 1. Voluntarily sign informed consent form. 2. \>=18 years of age at the time of signing informed consent. 3. Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1. 4. Diagnosis of MM with relapsed or refractory disease and have had at least 3 different prior lines of therapy including proteasome inhibitor (PI) (e.g., bortezomib or carfilzomib) immunomodulatory therapy (IMiD) (e.g., lenalidomide or pomalidomide), and anti-CD38 antibody therapy. 5. Participants must have measurable disease, including at least one of the criteria below: 1. Serum M-protein greater or equal to 0.5 g/dL. 2. Urine M-protein greater or equal to 200 mg/24 hours (h). 3. Serum free light chain (FLC) assay: involved FLC level of \>= 100 mg/L. 6. Adequate organ function, defined as: 1. Hemoglobulin \>8 gm/dl (transfusions allowed). 2. Platelets \>50,000/microliter (uL) (in the absence of platelet transfusion within 7 days of apheresis, but transfusion permitted prior to lymphodepleting chemotherapy). 3. Absolute neutrophil count (ANC) \> 1000/uL in the absence of growth factor support (filgrastim within 7 days or pegfilgrastim within 14 days of apheresis, but growth factor permitted prior to lymphodepleting chemotherapy). 4. Alanine aminotransferase (ALT)/aspartate aminotransferase (AST) =\< 3 x institutional upper limit of normal (ULN). 5. Total bilirubin =\< 1.5 mg/dl x institutional ULN, except with Gilbert's syndrome. 6. Serum creatinine clearance (CrCl) \>= 45 mL/min using Cockcroft-Gault formula. 7. Adequate cardiac function, defined as left ventricular ejection fraction (LVEF) \>= 40% as assessed by echocardiogram or multiple uptake gated acquisition (MUGA). 7. Women of childbearing potential (defined as all women physiologically capable of becoming pregnant) must have a negative serum or urine pregnancy test AND agree to use highly effective methods of contraception for 1 year after the last dose of anti-BCMA CAR-T cells. 8. Males who have partners of childbearing potential must agree to use an effective barrier contraceptive method. Exclusion Criteria: 1. Autologous transplant within 6 weeks of planned CAR-T cell infusion. 2. Active other malignancy, other than non-melanoma skin cancer, carcinoma in situ (e.g., cervix, bladder, or breast). Any fully treated malignancies or indolent, clinically insignificant malignancies can be discussed among the study team to determine eligibility. 3. HIV seropositivity. 4. Serologic status reflecting active hepatitis B or C infection. Patients that are positive for hepatitis B core antibody, hepatitis B surface antigen (HBsAg), or hepatitis C antibody must have a negative polymerase chain reaction (PCR) prior to enrollment. (PCR positive patients will be excluded). 5. Participants with uncontrolled intercurrent illness including, but not limited to ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, uncontrolled cardiac arrhythmia, pulmonary abnormalities, or psychiatric illness/social situations that would limit compliance with study requirements. 6. Pregnant or breastfeeding women are excluded from this study because CAR-T cell therapy may be associated with the potential for teratogenic or abortifacient effects. Because there is an unknown, but potential risk for adverse events in nursing infants secondary to treatment of the mother with CAR-T cells, breastfeeding should be discontinued. These potential risks may also apply to other agents used in this study. NOTE: Women of childbearing potential must have a negative serum or urine pregnancy test. 7. Patients with currently symptomatic central nervous system (CNS) pathology such as epilepsy, seizure disorders, paresis, aphasia, uncontrolled cerebrovascular disease, severe brain injuries, dementia, and Parkinson's disease. 8. History of autoimmune disease (e.g., rheumatoid arthritis, systemic lupus erythematosus) with requirement of immunosuppressive medication within 6 months. Eligibility for Infusion of Investigational Product: Participants will undergo an evaluation of eligibility on day -1 or 1 prior to infusion of anti-BCMA CAR-T cell product. This eligibility criteria will include the inclusion and exclusion criteria required for enrollment with the following exceptions and additions: 1. Hematologic function parameters will not be included as a pre-infusion eligibility criterion (because lymphodepletive chemotherapy is expected to cause pancytopenia). 2. Laboratory result abnormalities that are considered not clinically significant by the principal investigator AND are not the result of a demonstrated active infection or an active central nervous system condition. Exclusion criteria additions: 1. Use of anti-multiple myeloma therapy, including systemic corticosteroids within 14 days prior to lymphodepletive chemotherapy. 2. Neurologic symptoms suggestive of an active central nervous system condition.