• Subjects must have histologically confirmed myeloma relapsed or refractory after 3 or more lines of therapy including an immunomodulatory agent, a proteasome inhibitor and an anti-CD38 antibody. Failing line of therapy is defined accordingly to International Myeloma Workshop Consensus Panel.

• No evidence of CNS myeloma.

• Male or female \> 18 years of age.

• ECOG Performance status ≤ 2.

• Has measurable disease at the time of enrollment as defined by at least one of the following:

‣ Serum M-protein greater or equal to 0.5g/dL

⁃ Urine M-protein greater or equal to 200mg/24hr

⁃ Serum free light chain (FLC) assay: involved light chain greater or equal to 10mg/dL provided serum FLC ratio is abnormal

⁃ Bone marrow plasma cells greater than or equal to 30% total bone marrow cells

• \>2 weeks since prior radiation therapy or systemic therapy at the time of leukapheresis.

• Total bilirubin ≤ 1.5 mg/dL (except in patients with Gilbert's syndrome).

• AST (SGOT)/ALT ≤ 2.5 X institutional upper limit of normal.

• Serum creatinine \< 2 mg/dL.

⁃ Cardiac ejection fraction of \>45%, and no evidence of pericardial effusion, as determined by an echocardiogram.

⁃ Adequate pulmonary function as defined as pulse oximetry ≥ 92% on room air.

⁃ Subjects (or legal guardians) must have the ability to understand and the willingness to sign a written informed consent document.

⁃ For women of childbearing potential: agreement to remain abstinent (refrain from heterosexual intercourse) or use a contraceptive method with a failure rate of \< 1% per year during the treatment period and for at least 90 days after the BAFF CAR-T cell infusion.

⁃ For men: agreement to remain abstinent (refrain from heterosexual intercourse) or use contraceptive measures, and agreement to refrain from donating sperm