Inclusion Criteria:

• ≥ 18 years of age at the time of signing informed consent.
• Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1.
• 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.
• 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.
• For Part A (Dose Escalation) only:
  • Evidence of cell membrane BCMA expression, as determined by a validated immunohistochemistry (IHC) of formalin-fixed, paraffinembedded (FFPE) tumor tissue (e.g., bone marrow biopsies or plasmacytoma).
• Women of child-bearing potential (WCBP), defined as a sexually mature woman who has not undergone a hysterectomy or tubal ligation or who has not been naturally postmenopausal for at least 24 consecutive months, must have a negative serum pregnancy test prior to treatment. All sexually active WCBP and all sexually active male subjects must agree to use highly effective methods of birth control through one year post bb2121 infusion.
• Women of childbearing potential (WCBP) must:
  • Have a negative pregnancy test as verified by the Investigator, one negative serum beta human chorionic gonadotropin [β-hCG] pregnancy test result at screening, prior to LD chemotherapy. This applies even if the subject practices true abstinence* from heterosexual contact;
  • Either commit to true abstinence* from heterosexual contact or agree to use, and be able to comply with, effective measures of contraception without interruption, from screening through at least 1 year following last bb2121 infusion.  Contraception methods must include 1 highly effective and 1 additional effective (barrier) method of contraception from screening until at least 12 months following bb2121 infusion;
  • Agree to abstain from breastfeeding during study participation and for at least 1-year post-bb2121 infusion;
  • Refrain from tissue donation including egg donation or any other tissue/blood/organ donations, for at least 1 year following bb2121 infusion.
• Male subjects must:
  • Practice true abstinence* or agree to use a condom during sexual contact with a pregnant female or a female of childbearing potential for at least one year post BB2121 infusion, even if he has undergone a successful vasectomy. Subjects will be followed from screening until at least 1 year following last bb2121 infusion.
  • Refrain from tissue donation including sperm or any other tissue/blood/organ donation for at least 1 year following bb2121 infusion.
    • Note: Highly effective methods are defined as those that result in a low failure rate (i.e., less than 1% per year) when used consistently and correctly. The following are examples of highly effective and additional effective methods of contraception:
      • Intrauterine device (IUD);
      • Hormonal (birth control pill, injections, implants);
      • Bilateral tubal ligation;
      • Successful vasectomy;
      • Male condom (additional effective method);
      • Diaphragm (additional effective method);
      • Cervical cap (additional effective method).
• Recovery to ≤ Grade 1 or baseline of any non-hematologic toxicities due to prior treatments, excluding alopecia and Grade 2 neuropathy.
• * True abstinence is acceptable when this is in line with the preferred and usual lifestyle of the subject. Periodic abstinence (e.g., calendar, ovulation, symptothermal, post-ovulation methods) and withdrawal are not acceptable methods of contraception.
• Ability and willingness to adhere to the study visit schedule and all protocol requirements.
• Voluntarily sign informed consent form(s) (ICFs).

Exclusion Criteria:

• Treatment with the following therapies within the specified time period:
  • Any prior systemic therapy for MM within 14 days prior to scheduled protocolrequired leukapheresis;
  • Investigational cellular therapies within 8 weeks prior to the start of lymphodepletion (Note: Criterion 1c does not apply to subjects undergoing retreatment).
• Subjects with known central nervous system (CNS) disease. History or presence of clinically relevant CNS pathology such as epilepsy, seizure, paresis, aphasia, stroke, subarachnoid hemorrhage or CNS bleed, severe brain injuries, dementia, Parkinson’s disease, cerebellar disease, organic brain syndrome, or psychosis.
  • Note: this criterion does not apply to subjects undergoing retreatment unless Grade 4 neurotoxicity was observed following prior treatment with bb2121.
• Inadequate hepatic function defined by aspartate aminotransferase (AST) and/or alanine aminotransferase (ALT) > 2.5 × upper limit of normal (ULN) and direct bilirubin >1.5 × ULN.
• Inadequate renal function defined by creatinine clearance ≤5 ml/min using the Cockcroft-Gault formula.
• International ratio (INR) or partial thromboplastin time (PTT) > 1.5 × ULN.
• Inadequate bone marrow function defined by absolute neutrophil count (ANC) < 1000 cells/mm^3 in the absence of growth factor support (Neupogen within 7 days or Neulasta within 14 days) and platelet count < 50,000 cells/mm^3, in the absence of transfusion support (platelet transfusion within 7 days).
• Left ventricular ejection fraction < 50%.
• Ongoing treatment with chronic immunosuppressants (e.g., cyclosporine or systemic steroids at any dose). Intermittent topical, inhaled, or intranasal corticosteroids are allowed.
• Presence of active infection within 72 hours prior to leukapheresis or lymphodepletion; subjects with ongoing use of prophylactic antibiotics, antifungals, or antivirals are eligible as long as there is no evidence of active infection.
• Previous history of an allogeneic bone marrow transplantation or treatment with any gene therapy-based therapeutic for cancer.
• 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.
• Known human immunodeficiency virus (HIV) positivity.
• 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.
• 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; exceptions to this criterion include successfully treated non-metastatic basal cell or squamous cell skin carcinoma, or prostate cancer that does not require therapy.
• Subjects who have had a venous thromboembolic event (e.g., pulmonary embolism or deep vein thrombosis) requiring anticoagulation and who meet any of the following criteria:
  • Requires ongoing therapeutic anticoagulation;
  • Have had a Grade 2, 3, or 4 hemorrhage in the last 30 days;
  • Are experiencing continued symptoms from their venous thromboembolic event (e.g., continued dyspnea or oxygen requirement).
    • NOTE: Subjects who have had a venous thromboembolic event but do not meet any of the above 3 criteria are eligible for participation.
• Subjects who have plasma cell leukemia or clinically significant amyloidosis.
• Pregnant or lactating women.