Inclusion Criteria:

1. Patients with histologically confirmed MM with progressive disease according to the IMWG criteria 47 during or within 60 days of their last regimen who have received 1-3 lines of prior therapy (inclusive of a lenalidomide-containing regimen) and have measurable disease within 4 weeks of enrollment based on one of the following:

* Serum monoclonal protein ≥ 1.0 g/dL
* Urine monoclonal protein ≥ 200 mg/24 hour
* Involved serum immunoglobulin free light chains (FLC) ≥ 10 mg/dL AND abnormal kappa/lambda ratio.

Note: Because the primary endpoint is MRD-negativity rate, per the discretion of the Principal Investigator (PI), patients without measurable disease (e.g., M-spike \< 1.0 g/dL) may also be enrolled in line with the IMWG MM response criteria 47.
2. Prior treatment with cluster of differentiation 38 (CD38) -directed therapy is permitted only if all the following are fulfilled:

* Best response achieved during CD38-directed therapy was ≥ PR.
* Patient did not progress while receiving CD38-directed therapy or within 60 days of last dose of therapy.
* Patient did not discontinue CD38-directed therapy due to a related AE.
3. Prior treatment with carfilzomib is permitted only if all the following are fulfilled:

* Best response achieved during carfilzomib-based therapy was ≥ PR.
* Patient did not progress while receiving carfilzomib-based therapy or within 60 days of last dose of therapy.
* Patient did not discontinue carfilzomib due to a related AE.
4. Creatinine Clearance (CrCl) ≥60 ml/min measured within 4 weeks of enrollment. CrCl can be measured or estimated using Cockcroft-Gault method, Modification of Diet in Renal Disease (MDRD), or Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) formulae.
5. Age ≥ 18 years at the time of signing the informed consent documentation. Age limit of 75 years.
6. Eastern Cooperative Oncology Group (ECOG) performance status 0-2 within 4 weeks of enrollment (Appendix A).
7. Absolute neutrophil count (ANC) ≥ 1.0 K cells/µL, hemoglobin ≥ 8 g/dL, and platelet count ≥ 50 K platelets/µL measured within 4 weeks of enrollment unless cytopenias are deemed to be due to disease at the discretion of the clinical Investigator. Transfusions and administration of growth factors are permissible.
8. Adequate hepatic function with bilirubin \< 1.5 x the upper limit of normal (ULN) and aspartate aminotransferase (AST) and alanine aminotransferase (ALT) \< 3.0 x ULN measured within 4 weeks of enrollment.
9. All study participants must be able to tolerate one of the following thromboprophylactic strategies: oral factor Xa inhibitors or low molecular weight heparin or alternative anti-coagulant.
10. Females of childbearing potential (FCBP)† must have a negative serum or urine pregnancy test within 10-14 days and again within 24 hours prior to prescribing of iberdomide for Cycle 1 (prescriptions must be filled within 7 days) 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 (barrier) method, at the same time at least 28 days before she starts taking iberdomide without interruption. 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.

* A FCBP is a female who: 1) has achieved menarche at some point, 2) has not undergone a hysterectomy or bilateral oophorectomy, or 3) has not been naturally postmenopausal (amenorrhea following cancer therapy does not rule out childbearing potential) for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months). Females who do not meet the above definition of FCBP should be classified as females not of childbearing potential (FNCBP).

Exclusion Criteria:

1. Patients receiving concurrent systemic treatment for MM with the following exceptions:

* Treatment of hypercalcemia or spinal cord compression or aggressively progressing myeloma with current or prior corticosteroids is permitted.
* Patients may receive kyphoplasty/vertebroplasty for symptomatic vertebral compression fractures.
* Bone targeting agents are permitted.
* Concurrent or prior treatment with corticosteroids for indications other than MM is permitted.
* Focal radiation therapy within 14 days prior to randomization with the exception of palliative radiotherapy for symptomatic management but not on measurable extramedullary plasmacytoma.
* Prior MM treatments must be concluded with a washout period of 2 weeks from last dose.
2. Patients who are refractory to an anti-CD38-directed regimen:

* Prior anti-CD38-directed therapy and carfilzomib are permitted as long as above inclusion criteria are met.
3. Patients with plasma cell leukemia.
4. Patients with Polyneuropathy, Organomegaly, Endocrinopathy, Monoclonal protein, Skin changes syndrome (POEMS syndrome).
5. Patients with amyloidosis.
6. Patients with known chronic obstructive pulmonary disease (COPD) with a forced expiratory volume in 1 second (FEV1) \< 50% of predicted normal within 4 weeks of enrollment.

Note: FEV1 testing is required for patients suspected of having COPD, and patients must be excluded if FEV1 \< 50% of predicted normal at any time during the study.
7. Pregnant or lactating females. Because there is a potential risk for AEs in nursing infants secondary to treatment of the mother with carfilzomib in combination with iberdomide, pregnant or lactating females are excluded from study participation. These potential risks may also apply to other agents used in this study.
8. Uncontrolled hypertension (ie, systolic blood pressure \[BP\] \> 160 mmHg, diastolic BP \> 100 mmHg) or diabetes
9. Patients with active hepatitis B or C infection.
10. Patient is:

* Seropositive for human immunodeficiency virus (HIV) (Section 10.3.5.1) within 4 weeks of enrollment.
* Seropositive for hepatitis B (defined by a positive test for hepatitis B surface antigen \[HBsAg\]) within 4 weeks of enrollment. Patients with resolved infection (i.e., patients who are HBsAg negative but positive for antibodies to hepatitis B core antigen (anti-HBc) and/or antibodies to hepatitis B surface antigen \[anti-HBs\]) must be screened using real-time polymerase chain reaction (RT-PCR) measurement of hepatitis B virus (HBV) DNA levels. Those who are PCR positive will be excluded. EXCEPTION: Patients with serologic findings suggestive of HBV vaccination (anti-HBs positivity as the only serologic marker) AND a known history of prior HBV vaccination do not need to be tested for HBV DNA by PCR.
* Seropositive for hepatitis C (except in the setting of a sustained virologic response (SVR), defined as aviremia at least 12 weeks after completion of antiviral therapy).

For more information regarding the timing and frequency of hepatitis testing, refer to Section 10.3.5.1.
11. Significant cardiovascular disease with New York Heart Association (NYHA) class III or IV symptoms, symptomatic ischemia, current uncontrolled arrhythmias, screening electrocardiogram (ECG) with corrected QT interval (QTc) of \> 470 msec within 4 weeks of enrollment, pericardial disease, or myocardial infarction within 4 months prior to enrollment, and left ventricular ejection fraction (EF) \< 40% as assessed by transthoracic echocardiogram (ECHO) within 4 weeks of enrollment. Current unstable angina as determined by history and physical exam, hypertrophic cardiomyopathy or restrictive cardiomyopathy
12. Pulmonary hypertension
13. Has refractory gastrointestinal (GI) disease with refractory nausea/vomiting, inflammatory bowel disease, or bowel resection that would prevent absorption of oral agents
14. Uncontrolled intercurrent illness including but not limited to active infection or psychiatric illness/social situations that would compromise compliance with study requirements
15. Significant neuropathy ≥ Grade 3 with pain at baseline
16. Contraindication to any concomitant medication, including antivirals or anticoagulation
17. Major surgery within 3 weeks prior to first dose
18. Prior treatment with iberdomide
19. For female patients: Patient plans to become pregnant or donate eggs during the Treatment Period and/or required period for contraception use post-last dose of study treatment.
20. For male patients: Patient plans to father a child or donate sperm during the Treatment Period and/or required period for contraception use post-last dose of study treatment.
21. Patients with limited decision-making capacity.