• Subject must have intermediate- or high risk smoldering multiple myeloma (SMM) as confirmed by at least one of the following factors either at screening or within 28 days of screening:

‣ Bone marrow clonal plasma cells \>= 20% confirmed on either screening bone marrow biopsy or by outside pathology ≤5 years from initiation of study drug.

⁃ Abnormal serum free light chain ratio \> 20 by serum free light chain (FLC) assay

⁃ Serum monoclonal protein \>= 2 g/dL

• Subject must have been diagnosed with SMM =\< 5 years from initiation of study drug

• Both men and women of all races and ethnic groups are eligible for this study

• Eastern Cooperative Oncology Group (ECOG) performance status 0-2 (Karnofsky \>= 60%) is required for eligibility

• Absolute neutrophil count (ANC) \>= 1500/uL

• Hemoglobin (Hgb) \> 11 g/dL

• Platelet count \>= 100,000 cells/mm\^3 and must be platelet and packed red blood cells (PRBC) transfusion independent with no granulocyte colony-stimulating factor (G-CSF) to ensure eligibility within 8 weeks of screening

• Estimated creatinine clearance \>= 30 mL/min as defined by Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) or Cockcroft-Gault

• Total bilirubin \< 2 mg/dL except in subjects with congenital bilirubinemia such as Gilbert syndrome, in which case direct bilirubin =\< 2 times the institutional upper limit of normal is required

• Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) \< 2.5 times the institutional upper limit of normal

• Left ventricular ejection fraction \>= 40%

• Females of childbearing potential (FCBP) must have two negative pregnancy tests as verified by the investigator prior to starting study treatment. The effects of Iberdomide on the developing human fetus are unknown. For this reason, women of child-bearing potential 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. A FCBP must 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. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately

• Female of childbearing potential (FCBP) is a sexually mature woman who:

‣ Has not undergone a hysterectomy or bilateral oophorectomy; or

⁃ Has not been naturally postmenopausal for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months)

• The subject must be willing to comply with fertility requirements as below:

‣ Male subjects must agree to use an adequate method of contraception for the duration of the study and for 3 months afterwards

⁃ Female subjects must be either postmenopausal, free from menses \>= 2 years (yrs), surgically sterilized, willing to use two adequate barrier methods of contraception to prevent pregnancy, or agree to abstain from heterosexual activity starting with screening and for 3 months after last treatment in all patients

⁃ Patients must agree not to donate blood, sperm/ova while taking protocol therapy and for at least 4 weeks after stopping treatment

• Subject must understand and voluntarily sign an informed consent form (ICF) prior to any study-related assessments/procedures being conducted

• Subject is willing and able to adhere to the study visit schedule and other protocol requirements

• Subjects with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial