• PRE-REGISTRATION ELIGIBILITY CRITERIA (STEP 0):

• All patients must be pre-registered. For patients who consent to biobanking, submit the bone marrow and blood specimens

‣ Note: Patients who do not consent to the optional biobanking must be pre-registered, but specimens should not be submitted for these patients

⁃ Please ensure patient has suspected diagnosis of multiple myeloma and meets on study guidelines prior to informed consent and biospecimen collection

⁃ In cases where the bone marrow aspiration may be inadequate at Step 0 registration, the patient may still register on study

• ELIGIBILITY CRITERIA (STEP 1):

• Patients must have diagnostically confirmed MM in response status of stable disease or better by International Myeloma Working Group (IMWG) criteria at day 80-110 post-infusion of ide-cel. Patients in deep remission (e.g., CR, MRD-negative, etc.), are eligible

• All patients are required to have received ide-cel CAR-T within 80-110 days of registration

• Adverse events related to ide-cel are required to have resolved to grade =\< 1 except fatigue, alopecia, and other events that are unlikely to interfere with study assessments or pose a safety risk to participants

• Patients must have had ≥ 4 lines of therapy for MM (this includes proteasome inhibitor, immunomodulatory agent, and anti-CD38 monoclonal antibody)

• Prior therapy with iberdomide is permitted but prior iberdomide refractoriness is prohibited. Refractoriness is defined as per published IMWG criteria; progression while on iberdomide or within 60 days of stopping iberdomide

• Patients who have received MM-directed therapy since ide-cel infusion are not eligible, with the exception of short-course steroids for managing ide-cel toxicity as described below

• Age ≥ 18 years

• Eastern Cooperative Oncology Group (ECOG) performance status ≤ 2

• Absolute neutrophil count (ANC) ≥ 1,500/mm\^3

‣ Platelet transfusions or use of growth factors for neutropenia (e.g., filgrastim, tbo-filgrastim, sagramostim) are not permitted to meet enrollment criteria

• Platelet count ≥ 75,000/mm\^3

‣ Platelet transfusions or use of growth factors for neutropenia (e.g., filgrastim, tbo-filgrastim, sagramostim) are not permitted to meet enrollment criteria

• Calculated (calc.) creatinine clearance \>= 30 mL/min by Modification of Diet in Renal Disease (MDRD)

‣ Platelet transfusions or use of growth factors for neutropenia (e.g., filgrastim, tbo-filgrastim, sagramostim) are not permitted to meet enrollment criteria

• Total bilirubin ≤ 1.5 x upper limit of normal (ULN)

‣ Platelet transfusions or use of growth factors for neutropenia (e.g., filgrastim, tbo-filgrastim, sagramostim) are not permitted to meet enrollment criteria

• Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) ≤ 3 x upper limit of normal (ULN)

‣ Platelet transfusions or use of growth factors for neutropenia (e.g., filgrastim, tbo-filgrastim, sagramostim) are not permitted to meet enrollment criteria

• Not pregnant and not nursing, because this study involves an investigational agent whose genotoxic, mutagenic and teratogenic effect on the developing fetus and newborn are unknown.

‣ FCBP (female of childbearing potential) is a female who: 1) has achieved menarche (first menstrual cycle) at some point, 2) has not undergone a hysterectomy (the surgical removal of the uterus) or bilateral oophorectomy (the surgical removal of both ovaries) or 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 during the preceding 24 consecutive months).

⁃ Females of childbearing potential (FCBP):

• Must use a contraceptive method that is highly effective (with a failure rate of \< 1% per year), preferably with low user dependency during the intervention period and for at least 28 days after the last dose of study intervention and agrees 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 effects of iberdomide on the developing human fetus are unknown. Immunodulatory derivative (IMiD) agents as well as other therapeutic agents used in this trial are known to be teratogenic. Females of child-bearing potential (FCBP) must have a negative serum or urine pregnancy test with a sensitivity of at least 25 mIU/mL within 10-14 days prior to, and again within 24 hours of starting iberdomide, and must either commit to continued abstinence from heterosexual intercourse or begin two acceptable methods of birth control, one highly effective method and one additional effective method at the same time, at least 28 days before she starts taking iberdomide. Examples of highly effective methods are intrauterine device, hormonal contraceptives, tubal ligation, or partner's vasectomy. Examples of barrier method are male condom, diaphragm, or cervical cap. FCBP must also agree to ongoing pregnancy testing. Men must agree to use a latex condom during sexual contact with a FCBP even if they have had a successful vasectomy. All patients must be counseled at a minimum of every 28 days about pregnancy precautions and risk of fetal exposure.

∙ Should a woman become pregnant or suspect she is pregnant while she or her partner are participating in this study, she should inform her treating physician immediately. FCBP must use adequate contraception for at least 28 days after discontinuation from study. Because of the potential for serious adverse reactions in a breastfed child, women are advised not to breastfeed during treatment and for at least 28 days after the last dose.

∙ 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.

⁃ Non-childbearing 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

• Male patients must agree to use an adequate method of contraception for the duration of the study and for 28 days afterwards.

‣ Male participants: contraceptive use should be consistent with local regulations regarding the methods of contraception for those participating in clinical studies:

• Male participants are eligible to participate if they agree to the following during the intervention period and for 28 days after the last dose of study treatment to allow for clearance of any altered sperm:

⁃ Refrain from donating sperm

‣ PLUS, either:

• Be abstinent from heterosexual intercourse as their preferred and usual lifestyle (abstinent on a long term and persistent basis) and agree to remain abstinent OR

• Must agree to use contraception/barrier as detailed below:

‣ Agree to use a male condom, even if they have undergone a successful vasectomy, and female partner to use an additional highly effective contraceptive method with a failure rate of \< 1% per year as when having sexual intercourse with a woman of childbearing potential (including pregnant females)

• Patients may not have polyneuropathy, organomegaly, endocrinopathy, monoclonal gammopathy, and skin changes (POEMS) syndrome or amyloidosis involving any vital organ; amyloidosis found in skin or lymph nodes (non-vital organs), or incidental observation of amyloidosis on bone marrow biopsy, are both permissible. Plasma cell leukemia is permissible for study enrollment

∙ Patients 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

∙ Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months prior to registration are eligible for this trial

∙ For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated

∙ Patients with a history of hepatitis C virus (HCV) infection must have been treated and cured. Patients with HCV infection who are currently on treatment are eligible if they have an undetectable HCV viral load

∙ Patients may not have other, active infections at time of study registration. Recent infections are not exclusionary if antibiotics have been completed and infection is considered to be resolved / controlled. (Chronic maintenance antibiotics for prior infections, such as fungal, are permissible.)

∙ No known allergy to iberdomide

∙ No known medical condition causing an inability to swallow oral formulations of agents

∙ Patients receiving other active therapies for MM since ide-cel infusion are prohibited from participating in the study

∙ Corticosteroids used for the purpose of managing ide-cel toxicity (often neurotoxicity) soon after ide-cel administration are acceptable, provided that the participant will have been off corticosteroids for \> 30 days by cycle 1 day 1. Physiologically dosed chronic steroids are permitted

∙ Given the potential for interaction with iberdomide, patients who take strong CYP3A4 inducers or inhibitors may enroll after switching to a different agent and after an appropriate washout period for that particular medication, ideally three half-lives, prior to cycle 1 day 1