Inclusion Criteria:

* Male or female participants aged 18 years or older.
* Subjects must have multiple myeloma that is relapsed (defined as non-responsive or progressive disease while on therapy or within 60 days of last treatment in participants who had achieved a minimal response (MR) or better on prior therapy) after three or more lines of therapy including at least one proteasome inhibitor, one imide, and one anti-CD38 agent.
* Participants with multiple myeloma with comorbid amyloid, and/or extramedullary disease will be eligible.
* To be eligible for response assessment, participants must have measurable disease at the time of screening defined as serum protein electrophoresis M-spike greater than or equal to 0.5 g/dl, urine protein electrophoresis M spike greater than or equal to 200 mg/24 hr, or difference in involved free light chain level of greater than or equal to 10 mg/dl provided serum free light chain (FLC) ratio is abnormal.
* ECOG Performance status ≤ 2
* Minimum of 2 weeks since prior radiation therapy or systemic therapy to treat malignancy at the time of blood sample collection for CAR-T manufacturing unless treatment was investigational, in which case a minimum of 4 weeks since last treatment is required. Prior CAR-T therapy is acceptable if participants exhibited progression free survival of greater than 6 months post CAR-T infusion.
* Total bilirubin ≤ 2X institutional upper limit of normal (except in participants with Gilbert's syndrome).
* AST (SGOT)/ALT (SGPT) ≤ 2.5 X institutional upper limit of normal.
* Calculated creatinine clearance ≥ 30mL/min estimated by the Cockcroft - Gault formula.
* Cardiac ejection fraction of ≥45% as determined by an echocardiogram.
* Adequate pulmonary function, defined as ≤ Grade 1 dyspnea and oxygen saturation (SaO2) ≥ 92% on room air. If pulmonary function tests (PFTs) are performed based on the clinical judgment of the treating physician, participants with forced expiratory volume in 1 second (FEV1) ≥ 50% of predicted and diffusing capacity for carbon monoxide (DLCO) (corrected for hemoglobin) of ≥ 40% of predicted will be eligible.
* Participants (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 6 months after the UF-KUREBCMA CAR-T cell infusion. A woman is considered to be of childbearing potential if she is < 60 years old, postmenarcheal, has not reached a postmenopausal state (\< 12 continuous months of amenorrhea with no identified cause other than menopause), and has not undergone surgical sterilization (removal of ovaries and/or uterus). Examples of contraceptive methods with a failure rate of \< 1% per year include bilateral tubal ligation, male sterilization, hormonal contraceptives that inhibit ovulation, hormone-releasing intrauterine devices, and copper intrauterine devices. The reliability of sexual abstinence should be evaluated in relation to the duration of the clinical trial and the preferred and usual lifestyle of the participant. Periodic abstinence (e.g., calendar, ovulation, symptothermal, or postovulation methods) and withdrawal are not acceptable methods of contraception.
* For men: agreement to remain abstinent (refrain from heterosexual intercourse) or use contraceptive measures, and agreement to refrain from donating sperm, as defined below: With female partners of childbearing potential, men must remain abstinent or use a condom plus an additional contraceptive method that together result in a failure rate of \< 1% per year during the treatment period and for at least 6 months after the UF-KURE-BCMA CAR-T cell infusion. Men must refrain from donating sperm during this same period. With pregnant female partners, men must remain abstinent or use a condom during the treatment period and for at least 6 months after the UF-KURE-BCMA CAR-T cell infusion to avoid potential embryonal or fetal exposure. The reliability of sexual abstinence should be evaluated in relation to the duration of the clinical trial and the preferred and usual lifestyle of the participant. Periodic abstinence (e.g., calendar, ovulation, symptothermal, or postovulation methods) and withdrawal are not acceptable methods of contraception.

Exclusion Criteria:

* Autologous stem cell transplant within 6 weeks of informed consent.
* Active CNS involvement of multiple myeloma.
* Plasma cell leukemia
* History of allogeneic hematopoietic stem cell transplantation.
* Second active malignancy, other than non-melanoma skin cancer or carcinoma in situ (e.g. cervix, bladder, breast, stage 1 uterine cancer or localized prostate cancer).
* 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.
* Known human immunodeficiency virus infection or acquired immunodeficiency syndrome related illness.
* 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. 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 CAR-T cells, 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 the most recent bone marrow biopsy prior to initiation of therapy.
* Serologic status reflecting 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).
* Participants 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.
* Participants 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.
* History of active autoimmune disease (i.e. rheumatoid arthritis, systemic lupus erythematosus) with requirement of systemic immunosuppressive medications other than low dose steroids \[i.e. maximum of 15mg prednisone equivalent\] within the last 6 months.