Inclusion Criteria:

          -  18 years of age at the time of signing informed consent

          -  Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1

          -  Subjects must have measurable disease including at least one of the criteria below:

        Serum M-protein greater or equal to 0.5 g/dL Urine M-protein greater or equal to 200 mg/24
        h Serum free light chain (FLC) assay: involved FLC level greater or equal to 10 mg/dL (100
        mg/L) provided serum FLC ratio is abnormal -Women of child-bearing potential (WCBP) must
        have a negative serum pregnancy test prior to treatment and refrain from tissue donation
        including egg donation or any other tissue/blood/organ donations, for at least 1 year
        following bb2121 infusion. All sexually active WCBP and all sexually active male subjects
        must agree to use effective methods of birth control throughout the study. All sexually
        active males subjects must refrain from tissue donation including egg donation or any other
        tissue/blood/organ donations, for at least 1 year following bb2121 infusion.

        Part A:

        Diagnosis of MM with relapsed or refractory disease and have had at least 3 different prior
        lines of therapy including proteasome inhibitor (e.g., bortezomib or carfilzomib) and
        immunomodulatory therapy (IMiD; e.g., lenalidomide or pomalidomide), or have "double
        refractory" disease to a proteasome inhibitor and IMiD, defined as progression on or within
        60 days of treatment with these agents

        - Part B: Diagnosis of MM with relapsed or refractory disease with previous exposure to PI
        (e.g., bortezomib or carfilzomib), IMiDs (e.g., lenalidomide or pomalidomide), and
        daratumumab, and refractory (based on IMWG criteria) to their last line of therapy

        Exclusion Criteria:

          -  Subjects with known central nervous system disease

          -  Inadequate hepatic function

          -  Inadequate renal function

          -  Inadequate bone marrow function

          -  Presence of active infection within 72 hours

          -  Significant co-morbid condition or disease which in the judgment of the Investigator
             would place the subject at undue risk or interfere with the study; examples include,
             but are not limited to, cirrhotic liver disease, sepsis, recent significant traumatic
             injury, and other conditions

          -  Subjects with second malignancies in addition to myeloma if the second malignancy has
             required therapy in the last 3 years or is not in complete remission

          -  Subjects with a history of class III or IV congestive heart failure or non-ischemic
             cardiomyopathy, unstable angina, myocardial infarction, or ventricular arrhythmia
             requiring medication or mechanical control within the previous 6 months

          -  Known human immunodeficiency virus (HIV) positivity

          -  Subjects who have plasma cell leukemia or clinically significant amyloidosis

          -  Pregnant or lactating women