This is a phase 1, open-label study evaluating the safety, clinical pharmacology and clinical activity of TNB-383B, a BCMA x CD3 T-cell engaging bispecific antibody, in participants with relapsed or refractory MM who have received at least 3 prior lines of therapy. The study consists of 4 portions, a monotherapy dose escalation (Arm A) and a monotherapy dose expansion (Arm B), Monotherapy once every 4 weeks (Q4W) dosing (Arm E), Monotherapy once every 3 weeks (Q3W) dosing (Arm F). Arm A will evaluate the safety, tolerability, pharmacokinetic (PK) and pharmacodynamic (PD) profiles of escalating doses of single-agent TNB-383B, administered Q3W, in approximately 73 participants. Once the maximum tolerated dose (MTD) or recommended phase 2 dose, (RP2D) is identified in Arm A, Arm B will be initiated to further characterize the safety, tolerability, PK and PD profiles of the MTD/RP2D 2 dose expansion arms of 48 participants each. Dose A will be evaluated as a monotherapy Q4W, in Arm E to further characterize the safety, tolerability, PK and PD profiles of the MTD/RP2D 2 dose expansion arms of 20 participants. Dose C will be evaluated as a monotherapy, in Arm F to further characterize the safety, tolerability, PK and PD profiles of the MTD/RP2D 2 dose expansion arms of 25 participants.

Inclusion Criteria:

• Has received three or more prior lines of therapy with exposure to a proteasome inhibitor (PI), an immunomodulatory imide (IMiD) and an anti-CD38 monoclonal antibody.

• Must have adequate bone marrow function as defined in the protocol.

• Must have an estimated glomerular filtration rate >= 30 mL/min as estimated by the Modification of Diet in Renal Disease formula.

• Must have total bilirubin <= 1.5 × upper limit of normal ([ULN]; except if the subject has a known diagnosis of Gilbert's syndrome, in which case bilirubin must be < 3 x ULN).

• Serum calcium (corrected for albumin) at or below the ULN range.

• Has Measurable Disease, defined as at least 1 of the following:

  • Serum M-protein >= 0.5 g/dL (>= 5 g/L).
  • Urine M-protein >= 200 mg / 24h.
  • Serum free light chain (FLC) assay: Involved FLC level >= 10 mg/dl (>=100 mg/L) and an abnormal serum FLC ratio (< 0.26 or > 1.65).

• Has confirmed evidence of relapse/progression from the immediately prior MM therapy, or participant is relapsed/refractory to the immediately prior MM therapy.

• Consents to a fresh pretreatment bone marrow tumor biopsy or has adequate archival bone marrow tumor tissue that was collected within 6 months prior to screening and without intervening treatment.

Exclusion Criteria:

• Has been diagnosed or treated for another malignancy within 3 years of enrollment, with the exception of basal cell or squamous cell carcinoma of the skin, in situ malignancy, low-risk prostate carcinoma after curative therapy, or complete resection/curative therapy of an advanced malignancy.
• History of central nervous system involvement by their myeloma.
• History of Grade >= 3 peripheral neuropathy.
• History of plasma cell leukemia, polyneuropathy, organomegaly, endocrinopathy, monoclonal protein and skin changes (POEMS) syndrome, or amyloidosis.
• Has received another investigational drug within 21 days of enrollment.
• Has ever received BCMA-targeted therapy.
• Has received a autologous stem cell transplant within 12 weeks or an allogeneic stem cell transplant within 1 year of the first dose of study drug treatment.
• Has any medical or psychiatric condition which in the opinion of the investigator or study Medical Monitor places the participant at an unacceptably high risk for toxicities, could interfere with successful or safe delivery of therapy, or could interfere with evaluation of the investigational product or interpretation of participant safety or study results.
• Has received any therapy to treat cancer or undergone a major surgical procedure within 21 days, or within 5 half-lives of an anticancer drug, prior to the first dose of study treatment, whichever is shorter.
• Has known active infection Grade >= 2 requiring anti-infective treatment.
• Has a history of major cardiac abnormalities.
• Has unresolved adverse events as defined in the protocol.