A Study of Teclistamab and Mezigdomide in People With Multiple Myeloma

Inclusion Criteria: 1. Patients with relapsed or refractory multiple myeloma who have been treated with a proteasome inhibitor, an IMiD, and an anti-CD38 antibody. Patients who have been treated with at least 2 prior lines of therapy are eligible. Multiple myeloma is defined by the International Myeloma Working Group (IMWG) updated criteria. 2. Patients need to have measurable disease defined by one or more of the following: 1. Serum myeloma (M)-protein greater than or equal to 0.5 g/dL (5 g/L). 2. Urine M-protein greater or equal to 200 mg/24 h. 3. Involved light chain (either kappa or lambda) \>10 mg/dL with an abnormal kappa: lambda ratio 4. Plasmacytoma(s) that is new or definitely increased verified by imaging or biopsy. Increase is defined as a 50% and at least 1 cm increase as measured serially by the sum of the products of the cross-diameters of the measurable lesion. 5. A bone marrow biopsy demonstrating \>30% infiltration of clonal plasma cells. 3. Patients who have received prior BCMA-directed therapy \> 90 days prior including antibody drug conjugates or chimeric antigen receptor T-cell \[CAR T\] are eligible. BCMA presence on the cell surface should be confirmed in patients who have been treated with prior BCMA targeted therapies. Prior treatment with BCMA targeted bispecific antibodies is not allowed. 4. Patients who have received bispecific antibodies \>60 days prior with targets other than BCMA are eligible. 5. Patients who have received allogeneic stem cell transplantation \>6 months prior are eligible. 6. Age ≥18 years. 7. Eastern Cooperative Oncology Group (ECOG) Performance Status (PS) 0-1. PS-2 is permitted if PS is due solely to bone pain. 8. Fulfil the criteria for Adequate Organ System Function Based on Safety Assessments: Hematologic: * Hemoglobin ≥8 g/dL (without prior RBC transfusion within 7 days before the laboratory test; recombinant human erythropoietin use is permitted) * Absolute neutrophil count (ANC) ≥1.0 × 109/L (prior growth factor support is permitted but must be without support for 7 days for G-CSF or GM-CSF and for 14 days for pegylated-G-CSF) before the screening and laboratory test * Platelets ≥75 × 10\^9/L in participants in whom \<50% of bone marrow nucleated cells are plasma cells and ≥50×109 /L in participants in whom ≥50% of bone marrow nucleated cells are plasma cells (without transfusion support or thrombopoietin receptor agonist within 7 days before the screening laboratory test) Chemistry: * Total bilirubin ≤2 × ULN; except in subjects with congenital bilirubinemia, such as Gilbert syndrome (in which case if total bilirubin is \>2×ULN, then direct bilirubin ≤1.5×ULN is required) * AST and ALT ≤2.5 × ULN * eGFR ≥30 mL/min Calculated by CKD-EPI formula adjusted for body surface area (BSA): (mL/min/1.73 m2) x BSA/1.73) * Serum calcium corrected for albumin ≤14 mg/dL (≤3.5 mmol/L) or free ionized calcium ≤6. mg/dL (≤1.6 mmol/L) 9. Resolved acute effects of any prior therapy to baseline severity or CTCAE Grade ≤ 1, with the exception of peripheral neuropathy attributable to bortezomib. 10. Female participants: A female participant is eligible to participate if she is not pregnant or breastfeeding, and at least one of the following conditions applies: ° Is not a woman of childbearing potential (WOCBP) Nonchildbearing potential is defined as follows (by other than medical reasons): * ≥45 years of age and has not had menses for \>1 year * Patients who have been amenorrhoeic for \<2 years without history of a hysterectomy and oophorectomy must have a follicle stimulating hormone value in the postmenopausal range upon screening evaluation * Post-hysterectomy, post-bilateral oophorectomy, or post-tubal ligation. Documented hysterectomy or oophorectomy must be confirmed with medical records of the actual procedure or confirmed by an ultrasound. Tubal ligation must be confirmed with medical records of the actual procedure OR * Is a WOCBP and agrees to use two different contraceptive methods that are highly effective (with a failure rate of \<1% per year), preferably with low user dependency , during the intervention period and for at least 6 months after the last dose of study intervention. * WOCBP must have two negative serum or urine pregnancy tests with 10-14 days in between prior to treatment with mezigdomide. The latter must be within 15 days of starting mezigdomide. WOCBP must agree to use two highly effective methods of contraception (i.e. copper-containing intrauterine device, established use of oral, inserted, injected or implanted hormonal method of contraception, or male/female sterilization, etc. * WOCBP must agree not to donate eggs (ova, oocytes) for the purpose of reproduction during this period. The investigator should evaluate the effectiveness of the contraceptive method in relationship to the first dose of study intervention. The investigator is responsible for review of medical history, menstrual history, and recent sexual activity to decrease the risk for inclusion of a woman with a nearly undetected pregnancy. Pregnancy prevention while on mezigdomide treatment is All WOCBP must agree and adhere to all testing and contraception requirements in the mezigdomide Global Pregnancy Prevention Plan (PPP). Duration of contraception for WOCBP must be in accordance with the mezigdomide Global PPP 11. Male participants: Male participants are eligible to participate if they agree to the following: male participants must agree to practice complete abstinence or agree to use a condom during sexual contact with a pregnant partner or an WOCBP while taking mezigdomide, during dose interruptions, and for 28 days after the last dose of mezigdomide, even if they have undergone a successful vasectomy (ie, with documented azoospermia 90 days after the procedure). See mezigdomide Global PPP, Appendix 3. Male participants must agree not to donate sperm for the p