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.