Inclusion Criteria:

* Participant has given voluntary signed written informed consent before performance of any study-related procedure that is not part of normal medical care, with the understanding that consent may be withdrawn by the participant at any time without prejudice to their future medical care.
* Eastern Cooperative Oncology Group (ECOG) performance status ≤2 (see Appendix).
* Age ≥ 18 years
* Measurable disease of multiple myeloma as defined by at least one of the following:

* Serum monoclonal protein ≥ 0.5 g/dL. Patients with IgD disease and lower amounts of monoclonal protein may be permitted to enroll with PI approval
* ≥ 200 mg of monoclonal protein in the urine on 24-hour urine protein electrophoresis
* Serum free light chain (FLC) ≥ 100 mg/L (10 mg/dL) and abnormal serum free light chain ratio
* Previously treated relapsed and refractory multiple myeloma:

* Patients must have received at least three prior lines of therapy;
* Prior therapy including an immunomodulatory drug, proteasome inhibitor, and anti-CD38 antibody (either in separate regimens or within the same regimen); and
* Disease progression on, or within 60 days of completion of last therapy.
* ANC ≥ 1000/μL. G-CSF is not permitted within 14 days of screening.
* Platelet count ≥ 50,000/µL. Platelet transfusion and thrombopoietin receptor agonists are not permitted within 7 days of screening.
* Hemoglobin ≥ 8 g/dL. Red blood cell transfusions are permitted to meet eligibility criteria.
* Calculated creatinine clearance of ≥ 30 mL/min by Modified Diet in Renal Disease (MDRD) formula or Cockcroft-Gault formula
* Serum bilirubin values \< 1.5 x ULN. Isolated bilirubin x 1.5 x ULN is acceptable if bilirubin is fractionated and direct bilirubin \<35%. Patients with elevated bilirubin due to Gilbert's syndrome may be permitted with PI approval (e.g. total bilirubin \<3 mg/dL and normal direct bilirubin); and
* Serum aspartate transaminase (ALT) and aspartate transaminase (AST) values \< 2.5 × the upper limit of normal (ULN) of the institutional laboratory reference range.
* Must be able to comply with thromboembolism prophylaxis with e.g. acetylsalicylic acid (ASA), apixaban, rivaroxaban, lower molecular weight heparin, or equivalent.
* Females of childbearing potential (FCBP) must:

* Have 2 negative pregnancy tests as verified by the Investigator prior to starting study therapy. The subject must agree to ongoing pregnancy testing during the course of the study, and after end of study treatment. This applies even if the subject practices true abstinence from heterosexual contact.
* Either commit to true abstinence from heterosexual contact (which must be reviewed on a monthly basis and source documented) or agree to use and be able to comply with two reliable forms of contraception as defined by the Pregnancy Prevention Plan.
* Male subjects must follow the mezigdomide Pregnancy Prevention Plan (see Appendix).
* Agree to follow the lifestyle considerations in Section 3.4 regarding blood donation, hospitalization and being in proximity to the hospital, and driving or operating heavy machinery.

Exclusion Criteria:

* Participants who have had myeloma therapy or investigational drug within 2 weeks prior to start of treatment or those who have not recovered from adverse events due to agents administered more than 2 weeks earlier.
* Participants who are receiving any investigational agents.
* Prior therapy with mezigdomide or iberdomide.
* Prior therapy with anti-GPRC5D therapy (e.g. talquetamab).
* Prior therapy with bispecific antibody therapy within three months
* Prior therapy with gene-modified adoptive cell therapy (e.g. CAR T-cells, NK cells) within three months
* Plasmapheresis within seven days prior to start of study treatment.
* Primary refractory disease.
* Concomitant high dose corticosteroids. Low dose corticosteroids (maximum dose prednisone 10 mg/day or equivalent) are permitted if given for disorders other than myeloma, e.g. adrenal insufficiency, rheumatoid arthritis, etc.