Inclusion Criteria:

• Voluntarily sign informed consent form(s) prior to any study-related assessments/procedures being conducted.
• ≥ 18 years of age at the time of signing informed consent.
• Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1.
• For Part A: Diagnosis of MM with relapsed or refractory disease and have had at least 3 different prior lines of therapy including PI (e.g., bortezomib or carfilzomib) and immunomodulatory therapy (IMiD; e.g., lenalidomide or pomalidomide), or have "double refractory" disease to a PI and IMiD, defined as progression on or within 60 days of treatment with these agents.
• For Part B: Diagnosis of MM with relapsed or refractory disease and:
  • have had at least 3 different prior lines of therapy with previous exposure to PI (e.g., bortezomib or carfilzomib), IMiDs (e.g., lenalidomide or pomalidomide), and a CD38 antibody (Note: induction with or without hematopoietic stem cell transplant and with or without maintenance therapy is considered a single line of therapy);
  • have undergone at least 2 consecutive cycles of treatment for each therapy, unless PD was the best response to the therapy; and
  • refractory to their last line of therapy. Refractory is defined as documented progressive disease during or within 60 days (measured from the last dose) of completing treatment with the last anti-myeloma therapy before study entry.
• Subjects must have measurable disease, including at least one of the criteria below:
  • Serum M-protein greater or equal to 1.0 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 detected on ≥50% of malignant plasma cells from either a bone marrow biopsy or plasmacytoma determined by a validated IHC of formalin-fixed, paraffin-embedded (FFPE) tumor tissue.
• Women of child-bearing potential (WCBP), defined as a sexually mature woman who has not undergone a hysterectomy, bilateral oophorectomy, or tubal ligation or who has not been naturally postmenopausal (amenorrhea following cancer therapy does not rule out childbearing potential) for at least 24 consecutive months, must:
  • have a negative serum beta human chorionic gonadotropin (β-hCG) pregnancy test, as verified by the Investigator, at screening and Baseline; and
  • must agree to abstain from breastfeeding during study participation and for at least 1 year post-bb21217 infusion and until CAR T cells are no longer present by qPCR on 2 consecutive tests.
• All sexually active WCBP and all sexually active male subjects (even if he has undergone a successful vasectomy) must agree to use effective methods of birth control for at least 1 year post bb21217 infusion (heterosexual contact only).
  • NOTE: 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 effective methods of contraception:
    • Intrauterine device;
    • Hormonal (birth control pill, injections, implants);
    • Partner’s vasectomy.
• Recovery to ≤ Grade 1 or baseline of any non-hematologic toxicities due to prior treatments, excluding alopecia and Grade 2 neuropathy.
• Ability and willingness to adhere to the study visit schedule and all protocol requirements.

Exclusion Criteria:

• Treatment with an investigational cellular therapy within 8 weeks prior to the start of lymphodepletion.
• Subjects with known multiple myeloma CNS disease. History or presence of clinically relevant CNS pathology such as epilepsy, seizure, paresis, aphasia, stroke, subarachnoid hemorrhage or other CNS bleed, severe brain injuries, dementia, Parkinson’s disease, cerebellar disease, organic brain syndrome, or psychosis.
  • Note: The myeloma CNS criterion does not apply to subjects undergoing retreatment unless Grade 4 neurotoxicity was observed following prior treatment with bb21217.
• Inadequate hepatic function defined by AST and/or ALT > 2.5 × upper limit of normal (ULN) and total bilirubin > 1.5 × ULN (unless due to Gilbert’s syndrome and direct bilirubin is ≤ 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, or history of Grade ≥ hemorrhage within 30 days, or subject requires ongoing treatment with chronic, therapeutic dosing of anticoagulants (e.g., warfarin, low molecular weight heparin, or Factor Xa inhibitors).
• Inadequate bone marrow function defined by absolute neutrophil count (ANC) < 1000 cells/mm3 in the absence of growth factor support (filgrastim within 7 days or pegfilgrastim within 14 days), and untransfused platelet count < 50,000 mm^3 (platelet transfusion within 7 days).
• Echocardiogram with left ventricular ejection fraction < 45%.
• Ongoing treatment with chronic immunosuppressants (e.g., cyclosporine or systemic steroids at any dose). Intermittent topical, inhaled, or intranasal corticosteroids are allowed.
• Previous history of an allogeneic bone marrow transplantation, treatment with any gene therapy-based therapeutic for cancer, or BCMA-targeted therapy.
  • Note: this criterion does not apply to subjects undergoing retreatment.
• 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.
• Known hepatitis A virus (HAV), hepatitis B virus (HBV) or hepatitis C virus (HCV) positivity with evidence of ongoing infection. Note that subjects with positive anti-HAV IgM are not eligible; subjects with positive anti-HAV IgG are eligible. Subjects who have been vaccinated against hepatitis B [positive for hepatitis B surface antibody (HBsAb)] who are negative for other markers of prior hepatitis B infection [e.g., negative for hepatitis B core antibody (HBcAb)] are eligible. Subjects with past exposure to HBV [HBc Ab positive and/or HBe Ab positive] are also eligible for the study provided they have received an antiviral treatment, and are negative by assessment for HBV DNA for 6 months prior to treatment. Subjects with known HBV infection should have undetectable HBV viral load and be maintained on antiviral therapy to prevent HBV re-activation. Also note that subjects who are positive for anti-hepatitis C antibody are eligible as long as they have a negative HCV viral load.
• Active, uncontrolled, systemic bacterial, viral, or fungal infection within 72 hours of lymphodepletion,or infection requiring intravenous (IV) antimicrobials for management. Subjects with ongoing use of prophylactic antibiotics, antifungals, or antivirals are eligible as long as there is no evidence of active infection.
• Subjects with a history of class III or IV congestive heart failure or severe non-ischemic cardiomyopathy, unstable or poorly controlled angina, myocardial infarction, or ventricular arrhythmia 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, carcinoma in situ of the cervix, carcinoma in situ of the breast, or incidental histologic finding of prostate cancer (T1a or T1b using the TNM [tumor nodes, metastasis clinical staging system]), or prostate cancer that is curative .
• Inadequate pulmonary function defined as oxygen saturation (SaO2) < 92% on room air.
• Subjects who have a history of plasma cell leukemia, active plasma cell leukemia, Waldenstrom’s macroglobulinemia, POEMS syndrome (polyneuropathy, organomegaly, endocrinopathy, monoclonal protein, and skin changes), or clinically significant amyloidosis.
• Subjects who are pregnant or intend to become pregnant during participation in the study.
• Subject must meet the criteria for the available tumor burden slots when dosing by tumor burden.
• Subjects with known hypersensitivity to any component of bb21217 product, cyclophosphamide, fludarabine or tociluzimab.
• Subject has any significant medical condition, laboratory abnormality, or psychiatric illness that would prevent the subject form participating in the study.
• Subject has any condition that confounds the ability to interpret data from the study.