Study of Iberdomide in People With Multiple Myeloma Who Have Had an Autologous Hematopoietic Stem Cell Transplant (AHCT)

Inclusion Criteria: All Patients 1. Histologic confirmation of multiple myeloma by the enrolling institution. Cohort specific eligibility below. 2. Age 18-75 3. Karnofsky performance greater than or equal to 70. 4. Recovered to Grade 1 or baseline of any non-hematologic toxicities due to prior treatments, excluding Grade 2 neuropathy. 5. Laboratory criteria 1. Absolute neutrophil count (ANC) greater than or equal to 1,000/mm3 without filgrastim use in the prior 14 days. 2. Platelet count greater than 75,000/mm3 (without platelet transfusion in the previous 7 days or thrombopoietin mimetics in the previous 28 days) 3. Hemoglobin greater than 8 g/dL (without red blood cell transfusion in the previous 7 days) 4. Creatinine Clearance (CrCl) greater than or equal to 30 mL/min, measured or estimated by Cockcroft-Gault equation. 5. Corrected serum calcium less than or equal to 13.5 mg/dL 6. Serum aspartate aminotransferase (AST) or alanine aminotransferase (ALT) less than or equal to 2.5 x upper limit of normal (ULN) 7. Serum total bilirubin less than or equal to 2 x ULN. Patients who have been diagnosed with Gilbert's disease are permitted to exceed the defined bilirubin value of 2 x ULN 8. International ratio (INR) or partial thromboplastin time (PTT) less than 1.5 x ULN unless on therapeutic anticoagulation 6. Females of childbearing potential (defined below) have a negative serum pregnancy test with a sensitivity of at least 50 mIU/mL Cohort 1: 1. Received a single prior autoHCT with melphalan ≥ 140mg/m2 and a ≥ 2x106 CD34+ cells/kg (actual body weight) less than or equal to 15 months from initiation of systemic anti-myeloma therapy 2. Have been on lenalidomide maintenance at a dose of ≥ 5 mg every other day for at least 6 months. 3. Have achieved a VGPR or less to treatment by International Myeloma Working Group Criteria 4. Be within 15 months of their autoHCT Cohort 2: 1. Have received 2 to 3 prior lines of systemic anti-myeloma therapy +/- prior autoHCT. 2. Have had lenalidomide maintenance therapy after a line of treatment prior to the salvage autoHCT. 3. Have undergone salvage autoHCT consolidation with a high dose melphalan based conditioning regimen within the prior 2-6 months Pregnancy A female of childbearing potential (FCBP) is a female who: 1. has achieved menarche at some point 2. has not undergone a hysterectomy or bilateral oophorectomy 3. has not been naturally postmenopausal (amenorrhea following cancer therapy does not rule out childbearing potential) for at least 24 consecutive months (ie, has had menses at any time in the preceding 24 consecutive months) and must: 1. Have two negative pregnancy tests as verified by the Investigator prior to starting study treatment. She 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. 2. 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 forms of contraception: one highly effective, and one additional effective (barrier) measure of contraception without interruption 28 days prior to starting investigational product, during the study treatment (including dose interruptions), and for at least 28 days after the last dose of iberdomide Male subjects must practice complete abstinence (True abstinence is acceptable when this is in line with the preferred and usual lifestyle of the subject. Periodic abstinence \[eg calendar, ovulation, symptothermal or post-ovulation methods\] and withdrawal are not acceptable methods of contraception.) or agree to use a condom during sexual contact with a pregnant female or a FCBP while taking iberdomide, during dose interruptions and for at least 90 days following the last dose of iberdomide even he has undergone a successful vasectomy. Males must agree to refrain from donating sperm while on study treatment, during dose interruptions and for at least 90 days following last dose of study treatment. All subjects must agree to refrain from donating blood while on study treatment, during dose interruptions and for at least 28 days following the last dose of study treatment. All male and female subjects must follow all requirements defined in the Pregnancy Prevention Program. All subjects must: * Understand that iberdomide could have potential teratogenic risk. * Agree to abstain from donating blood while taking iberdomide and for 28 days following discontinuation of the iberdomide. * Agree not to share iberdomide with another person. * Other than the subject, FCBP and males able to father a child should not handle the IP or touch the capsules unless gloves are worn. * Be counseled about pregnancy precautions and risks of fetal exposure as described in the Pregnancy Prevention Plan. Exclusion Criteria: 1. Prior allogeneic hematopoietic stem cell transplant 2. Disease progression after most recent autoHCT prior to enrollment 3. Known active central nervous system (CNS) involvement with MM 4. Prior organ transplant requiring systemic immunosuppressive therapy 5. History of a thromboembolic event while on full anticoagulation during prior therapy with an immunomodulatory agent (IMiD) 6. Unwilling to take DVT prophylaxis while on iberdomide maintenance 7. History of greater than or equal to Grade 2 hemorrhage within 30 days of enrollment 8. History of plasma cell leukemia, Waldenstrom's macroglobulinemia, POEMS (polyneuropathy, organomegaly, endocrinopathy, monoclonal protein, and skin changes), or clinically significant amyloidosis 9. Ongoing treatment with chronic immunosuppressants (eg, cyclosporine or systemic steroids at any dose). Physiologic replacement, intermittent topical, inhaled or intranasal corticosteroids are allowed. 10. Seropositive for human immunodeficiency virus (HIV-1), chronic or active hepatitis B (defined as positive hepatitis B surface antigen (HepBSAg) or Hepatitis B core antibody (HepBcore Ab)) or C (Hep C Ab), or acute hepatitis A. If any history of exposure to hepatitis B or C, then PCR should be negative. 11. Prior malignancies except resected basal cell carcinoma or treated carcinoma in situ. Cancer treated with curative intent less than 5 years prior to enrollment will not be allowed unless approved by the MSK PI. Cancer treated with curative intent greater than 5 years prior to enrollment is allowed. 12. Subject has a history of anaphylaxis or hypersensitivity to thalidomide, lenalidomide, or pomalidomide 13. Uncontrolled bacterial, viral or fungal infections (currently taking medication and with progression or no clinical improvement) at time of enrollment. 14. Serious medical of psychiatric illness likely to interfere with participation on this clinical study 15. Unwilling or unable to provide informed consent 16. Unable or unwilling to return to the transplant center for treatment and follow up