Inclusion Criteria:

        Subjects must satisfy the following criteria to be enrolled in the study:

          1. Subject is ≥ 18 years of age at the time of signing the informed consent form (ICF)

          2. Subject has measurable disease, defined as:

               -  M-protein (serum protein electrophoresis [sPEP] or urine protein electrophoresis
                  [uPEP]): sPEP ≥ 0.5 g/dL or uPEP ≥ 200 mg/24 hours and/or

               -  Light chain MM without measurable disease in the serum or urine: Serum
                  immunoglobulin free light chain ≥ 10 mg/dL and abnormal serum immunoglobulin
                  kappa lambda free light chain ratio

          3. Subjects with one of the following cohort specific requirements:

             Cohort 1 RRMM subjects with ≥ 3 prior anti-myeloma treatment regimens:

               -  Subject must have received at least 3 prior anti-myeloma treatment regimens.
                  Note: induction with or without hematopoietic stem cell transplant and with or
                  without maintenance therapy is considered a single regimen

               -  Subject must have undergone at least 2 consecutive cycles of treatment for each
                  regimen, unless PD was the best response to the regimen

               -  Subject must have received prior treatment with a proteasome inhibitor, an
                  immunomodulatory agent and an anti-CD38 antibody

               -  Subject has evidence of PD on or within 60 days of the most recent prior
                  treatment regimen

               -  Subject achieved a response (minimal response [MR] or better) to at least 1 prior
                  treatment regimen

             Cohort 2 subjects with 1 prior anti-myeloma treatment regimen:

               -  Subject must have received only 1 prior anti-myeloma treatment regimen. Note:
                  induction with or without hematopoietic stem cell transplant and with or without
                  maintenance therapy is considered a single regimen

               -  Subject must have the following HR factors:

                  - R-ISS stage III AND

               -  Early relapse defined as:

             Cohort 2a: PD < 18 months since date of start of initial therapy. Initial therapy must
             contain induction, ASCT (single or tandem) and lenalidomide containing maintenance.

             Cohort 2b: PD < 18 months since date of start or initial therapy which must contain at
             minimum, a proteasome inhibitor, an immunomodulatory agent and dexamethasone Cohort
             2c: Subject must have received minimum 3 cycles of induction therapy which must
             contain at minimum, a proteasome inhibitor, an immunomodulatory agent and
             dexamethasone. Subjects must have had ASCT (single or tandem AND < VGPR (excluding PD)
             at first assessment between 70 to 110 days after last ASCT, with initial therapy
             without consolidation and maintenance.

          4. Subject must have Eastern Cooperative Oncology Group (ECOG) performance status ≤ 1

          5. Subject must have recovery to Grade 1 or baseline of any non-hematologic toxicities
             due to prior treatments, excluding alopecia and Grade 2 neuropathy

        Exclusion Criteria:

        The presence of any of the following will exclude a subject from enrollment:

          1. Subject used any investigational agents within 14 days of leukapheresis

          2. Subject received any of the following within the last 14 days of leukapheresis:

               1. Plasmapheresis

               2. Major surgery (as defined by the investigator)

               3. Radiation therapy other than local therapy for myeloma associated bone lesions

               4. Use of any systemic anti-myeloma drug therapy

          3. Subject with known central nervous system involvement with myeloma

          4. Subject has clinical evidence of pulmonary leukostasis and disseminated intravascular
             coagulation

          5. History or presence of clinically relevant central nervous system (CNS) pathology

          6. Subject with active or history of plasma cell leukemia, Waldenstrom's
             macroglobulinemia, POEMS syndrome, or clinically significant amyloidosis

          7. Inadequate organ function Subject with a history of Class III or IV congestive heart
             failure (CHF) or severe nonischemic cardiomyopathy, unstable or poorly controlled
             angina, myocardial infarction, or ventricular arrhythmia within the previous 6 months
             prior to starting study treatment

          8. Ongoing treatment with chronic immunosuppressants

          9. Previous history of an allogeneic hematopoietic stem cell transplantation or treatment
             with any gene therapy-based therapeutic for cancer or investigational cellular therapy
             for cancer or BCMA targeted therapy

         10. Subject has received ASCT within 12 weeks prior to leukapheresis

         11. Subject has history of primary immunodeficiency

         12. Subject is positive for human immunodeficiency virus (HIV-1), chronic or active
             hepatitis B or active hepatitis A or C

         13. Subject has uncontrolled systemic fungal, bacterial, viral or other infection
             (including tuberculosis) despite appropriate antibiotics or other treatment

         14. Subject with prior history of malignancies, other than MM, unless the subject has been
             free of the disease for ≥ 5 years

         15. Pregnant or lactating women

         16. Subject with known hypersensitivity to any component of bb2121 product,
             cyclophosphamide, fludarabine, and/or tocilizumab