Inclusion Criteria:

1. Voluntarily sign informed consent form.
2. Age ≥18 years.
3. Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1.
4. Diagnosis of multiple myeloma (per IMWG criteria) with relapsed or refractory disease and has received at least 3 prior lines of therapy including proteasome inhibitor immunomodulatory therapy, and anti-Cluster of differentiation 38 (CD38) antibody therapy.
5. Participants may have received BCMA targeted therapy and must be at least 6 months from last BCMA therapy.
6. Participants must have documented evidence of progressive disease within 12 months of the last line of therapy or be refractory/nonresponsive to their most recent line.
7. Participants must have measurable disease, defined as at least one of the criteria below:

* Serum M-protein greater or equal to 0.5 grams per deciliter (g/dL).
* Urine M-protein greater or equal to 200 milligrams, over a 24-hour period (mg/24 h).
* Serum free light chain (FLC) assay: involved FLC level of ≥ 100 milligrams per liter (mg/L).
8. Adequate organ function, defined as:

* Adequate bone marrow function for apheresis and lymphodepleting chemotherapy.
* Hgb \>8 gm/dl (transfusions allowed).
* Platelets \>50,000/microliter (uL) (in the absence of platelet transfusion within 7 days of apheresis, but transfusion permitted prior to lymphodepleting chemotherapy).
* 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). For those patients who have evidence of duffy null, ANC \>750/uL is allowed.
* Absolute lymphocyte count (ALC) \>300/uL.
* Alanine aminotransferase/aspartate aminotransferase (ALT/AST) \< 3 x institutional upper limit of normal (ULN) and Total bilirubin \< 1.5 milligrams per deciliter (mg/dl) x institutional ULN, except with Gilbert's syndrome.
* Serum creatinine clearance (CrCl) ≥ 30 milliliter per minute (mL/min) using Cockcroft-Gault formula or as measured with a 24 hour urine collection.
* Adequate cardiac function, defined as left ventricular ejection fraction (LVEF) \> 40% as assessed by echocardiogram or multiple uptake gated acquisition (MUGA) and adequate pulmonary function (measured by room air pulse oximetry ≥ 92%).
9. Women of childbearing potential 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.
10. Males who have partners of childbearing potential must agree to use an effective barrier contraceptive method for 6 months after CAR-T therapy.

Exclusion Criteria:

1. Autologous transplant within 12 weeks of planned CAR-T cell infusion.
2. Prior antitumor therapy as follows, prior to apheresis:

* Investigational therapy within 14 days, or at least 5 half-lives.
* Monoclonal antibody therapy within 21 days.
* Cytotoxic therapy within 14 days.
* Proteasome inhibitor therapy within 14 days.
* Immunomodulatory therapy within 14 days.
* Radiotherapy within 14 days - with the exception that if radiotherapy (XRT) covers \<5% of marrow reserve - no rest window needed.
3. Toxicity from previous anticancer therapy must resolve to baseline levels or to Grade 1 or less except for alopecia, peripheral neuropathy and baseline hematologic toxicity that otherwise meets inclusion.
4. Active CNS multiple myeloma, plasma cell leukemia, primary AL amyloidosis or POEMS syndrome.
5. 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.
6. HIV seropositivity.
7. Serologic status reflects active hepatitis B or C infection. Participants 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 participants will be excluded).
8. 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.
9. 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.
10. Participants 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 OR seizure or stroke within 6 months.
11. History of autoimmune disease (e.g., rheumatoid arthritis, systemic lupus erythematosus) with requirement of immunosuppressive medication within 6 months.