Inclusion Criteria:

• 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

Exclusion Criteria:

• ASCT within 6 weeks of informed consent.
• History of allogeneic hematopoietic stem cell transplantation.
• Active graft-versus-host disease.
• Active central nervous system or meningeal involvement by myeloma. Subjects with untreated brain metastases/CNS disease will be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events. Patients with a history of CNS or meningeal involvement must be in a documented remission by CSF evaluation and contrast-enhanced MRI imaging for at least 90 days prior to registration.
• Active malignancy, other than non-melanoma skin cancer or carcinoma in situ (e.g. cervix, bladder, breast).
• Less than 28 days elapsed between prior treatment with investigational agent(s) and the day of lymphocyte collection.
• New York Heart Association class IV congestive heart failure.
• Cardiovascular disorders including unstable angina pectoris, clinically significant cardiac arrhythmias, myocardial infarction or stroke (including transient ischemic attack, or other ischemic event) within 6 months prior to registration.
• Active infection requiring intravenous systemic treatment.
• HIV seropositivity.
• Pregnant or breastfeeding women are excluded from this study because LMY-920 therapy may be associated with the potential for teratogenic or abortifacient effects. Women of childbearing potential must have a negative serum pregnancy test. Because there is an unknown, but potential risk for adverse events in nursing infants secondary to treatment of the mother with LMY-920, breastfeeding should be discontinued. These potential risks may also apply to other agents used in this study.
• Evidence of myelodysplasia or cytogenetic abnormality indicative of myelodysplasia on any bone marrow biopsy prior to initiation of therapy.
• 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.)
• Patients with history of clinically relevant CNS pathology such as epilepsy, seizure disorders, paresis, aphasia, uncontrolled cerebrovascular disease, severe brain injuries, dementia and Parkinson's disease.
• Subjects with uncontrolled intercurrent illness including, but not limited to ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, pulmonary abnormalities or psychiatric illness/social situations that would limit compliance with study requirements.
• Known additional malignancies which require systemic treatment.
• History of autoimmune disease (i.e. rheumatoid arthritis, systemic lupus erythematosus) with requirement of immunosuppressive medications (other than low dose steroids) within 6 months.