Dose Exploration Study OF JWCAR129, BCMA-Targeted CART for RRMM

Inclusion Criteria: 1. 18 years old and above. 2. Signed the Informed Consent Form. 3. Diagnosis of multiple myeloma (MM) with relapsed and/or refractory disease. Subjects must have received at least 3 prior anti-myeloma treatment regimens (note: induction with or without bone marrow transplant and with or without maintenance therapy is considered one regimen). Subjects must be refractory to the last anti-myeloma treatment regimen prior to entering the study. 1. Autologous hematopoietic stem cell transplantation. 2. A regimen that included an immunomodulatory agent (eg, thalidomide, lenalidomide, pomalidomide) and a proteasome inhibitor (eg, bortezomib, carfilzomib, ixazomib), either alone or in combination. Subjects must have undergone at least 2 consecutive cycles of treatment for each regimen unless progressive disease was the best response to the regimen. 3. Anti-CD38 (eg, daratumumab) as part of a combination regimen or as a monotherapy. Subjects who were not candidates to receive one or more of the above treatments (ie, contraindicated) are eligible; the reason for not receiving treatment must be clearly documented in the case report form. 4. Subjects must have measurable disease. 5. Subject must be willing to provide fresh bone marrow biopsy samples during Screening (and prior to study treatment, if required). 6. Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1 7. Adequate renal, bone marrow, hepatic, pulmonary, and cardiac function Exclusion Criteria: 1. Subjects with known active or history of CNS involvement by malignancy 2. Subjects with solitary plasmacytoma; active or history of plasma cell leukemia (PCL); Waldenstrom's macroglobulinemia; Polyneuropathy, Organomegaly, Endocrinopathy, Monoclonal plasmaproliferative disorder, Skin changes (POEMS) syndrome; or symptomatic amyloidosis 3. History of another primary malignancy that has not been in remission for at least 3 years. The following are exempt from the 3-year limit: non-melanoma skin cancer, curatively treated localized prostate cancer, cervical carcinoma in situ on biopsy or a squamous intraepithelial lesion on Pap smear, and in situ breast cancer that has been completely resected. 4. Require systemic immunosuppressive therapies (eg, calcineurin inhibitors, methotrexate, mycophenolate, rapamycin, thalidomide, immunosuppressive antibodies such as anti-IL-6 or anti-IL-6 receptor \[IL-6R\]) 5. Prior CAR T-cell or other genetically-modified T-cell therapy 6. Prior treatment with a BCMA-targeted agent 7. History or presence of clinically relevant CNS pathology such as epilepsy, seizure, paresis, aphasia, stroke, severe brain injuries, dementia, Parkinson's disease, cerebellar disease, organic brain syndrome, or psychosis 8. Untreated or active infection at time of initial screening, at the time of leukapheresis, within 72 hrs before lymphodepletion, or 5 days before JWCAR129 infusion. 9. History of any of the following cardiovascular conditions within 6 months of initial screening: Class III or IV heart failure as defined by the New York Heart Association (NYHA), myocardial infarction, unstable angina, uncontrolled or symptomatic atrial arrhythmias, any ventricular arrhythmias, or other clinically significant cardiac disease 10. History of severe immediate hypersensitivity reaction to any of the protocol-mandated or recommended agents used in this study 11. Allogeneic hematopoietic stem cell transplantation.