A Phase I/II Study of the Safety, Tolerability and Efficacy of Belantamab Mafodotin (GSK2857916) in Combination With Iberdomide (CC-220)/Dexamethasone Versus Belantamab Mafodotin (GSK2857916)/Dexamethasone in Relapsed Refractory Multiple Myeloma

* Documentation of disease: Diagnosis of multiple myeloma and have relapsed or refractory disease according to the IMWG criteria where: * Progression of myeloma is defined by IMWG criteria as recurrence of disease after prior response, indicated as any of the following: * ≥ 25% increase in M-protein (must be at least 0.5g/dl above nadir from last treatment regimen). * 25% difference between involved and uninvolved serum free light chains from its nadir or * The development of new plasmacytomas or hypercalcemia. * Refractory myeloma as defined by IMWG criteria as disease which become non-responsive or progresses on therapy or within 60 days of last treatment in patients who had achieved a minimal response or better on prior therapy. * Measurable disease defined by IMWG criteria as: * Serum M-protein ≥ 0.5 g/dL. * Urine monoclonal protein ≥ 200 mg/24h. * Serum free light chains (FLC) assay: Involved FLC level ≥ 10 mg/dl (≥ 100 mg/l) and serum free light chain ratio is abnormal. * Two or more prior lines of therapies, triple-class exposed (exposed /refractory to an immunodulatory derivative (IMiD) and/or proteasome inhibitors (PI) and/or to daratumumab or other anti-CD38 monoclonal antibody). * No prior exposure to iberdomide or belamaf. * No prior BCMA-directed therapy. * No prior treatment with a monoclonal antibody within 2 weeks of registration. * No history of severe allergic reaction (including erythema nodosum) to lenalidomide, pomalidoimide or other prior IMiD therapy. * No prior allogeneic stem cell transplant. NOTE: Participants who have undergone syngeneic transplant will be allowed only if no history of or no currently active GvHD. * Participant must not have received a live or live-attenuated vaccine within 30 days prior to registration. * No plasmapheresis within 7 days prior to registration. * Age ≥ 18 years. * Eastern Cooperative Oncology Group (ECOG) performance status ≤ 2. * Absolute neutrophil count (ANC) ≥ 1,000/mm\^3. * Platelet count ≥ 75,000/mm\^3 (or ≥ 50,000/mm\^3 in Phase II if bone marrow (BM) plasma cells \> 50%). * Calculated (Calc.) creatinine clearance ≥ 30 mL/min using Cockcroft-Gault equation. * Spot urine (albumin/creatinine ratios) \< 500 mg/g (56 mg/mmol) OR urine dipstick ≥ 1+ if confirmed. * Total bilirubin ≤ 2 mg/dL. * Aspartate aminotransferase (AST)/alanine transaminase (ALT) ≤ 2.5 x upper limit of normal (ULN). * 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). Women of childbearing potential (WOCBP): * 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 4 months 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 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 4 months 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 3 months 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. Nonchildbearing 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 6 months 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 6 months 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). * Archival tissue must be available for submission for the mandatory correlative studies. * 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. \* Patients with treated brain metastases are eligible if follow up brain imaging after central nervous system (CNS) directed therapy shows no evidence of progression. * No patients with uncontrolled human immunodeficiency virus (HIV), hepatitis C and B. Testing for HIV and hepatitis C and B are not required prior to registration. \* HIV-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial. * No positive hepatitis C antibody test result or positive hepatitis C ribonucleic acid (RNA) test result at screening or within 3 months prior to registration unless the participant can meet the following criteria: * RNA test negative. * Successful anti-viral treatment (usually 8 weeks duration) is required, followed by a negative hepatitis C virus (HCV) RNA test after a washout period of at least 4 weeks. * Patients with hepatitis B will be excluded unless the following criteria can be met. * Serology: Hepatitis B core antibody positive (HbcAb)+, hepatitis B surface antigen (HbsAg)-. * Screening: Hepatitis B virus (HBV) deoxyribonucleic acid (DNA) undetectable. * During study treatment: Monitoring per protocol. * During study treatment: Antiviral treatment instituted if HBV DNA becomes detectable. * Serology: HBsAg+ at screen or within 3 months prior to registration. * Screening: HBV DNA undetectable. * Screening: Highly effective antiviral treatment started at least 4 weeks prior to first registration. * Screening: Baseline imaging per protocol. * Screening: Participants with cirrhosis are excluded. * During study treatment: Antiviral treatment maintained throughout study treatment. * During study treatment: Monitoring and management per protocol. \*\* Note: Presence of isolated hepatitis (Hep) B surface antibody (HBsAb) indicating previous vaccination will not exclude a participant. * No patients with unacceptable cardiac risk factors defined by any of the following criteria: * Evidence of current clinically significant uncontrolled arrhythmias, including clinically significant electrocardiogram (ECG) abnormalities such as 2nd degree (Mobitz Type II) or 3rd degree atrioventricular (AV) block. * History of myocardial infarction, acute coronary syndromes (including unstable angina), coronary angioplasty, or stenting or bypass grafting within three (3) months of Screening. * Class III or IV heart failure as defined by the New York Heart Association functional classification system \[Error! Reference source not found., 1994\]. * Uncontrolled hypertension. * Patients with congenital long QT syndrome, QTcF interval QTcF \> 480 msec (the QT interval values must be corrected for heart rate by Fridericia's formula \[QTcF\]). * Any history of ventricular fibrillation or torsade de pointes. * Symptomatic bradycardia defined as heart rate (HR) \< 50 bpm with associated dizziness/syncope. * Left ventricular ejection fraction \< 30%. * No patients who have received targeted (non-monoclonal antibodies \[mAb\]) or investigational agents within 2 weeks prior to rgistration and who have not recovered from side effects of those therapies. * No patients who have undergone major surgery ≤ 2 weeks prior to registration or who have not recovered from the side-effects of surgery. * No known medical condition causing an inability to swallow oral formulations of agents. * No active bacterial, viral or fungal infection (s) present. * Patients cannot have a Child-Pugh score greater than 1 (absent ascites, total bilirubin \< 2, international normalized ratio (INR) \<1.7 (unless on anticoagulation), and no encephalopathy; esophageal or gastric varices, and cirrhosis. Note: Stable non-cirrhotic chronic liver disease (including Gilbert's syndrome or asymptomatic gallstones) or hepatobiliary involvement of malignancy is acceptable if otherwise meets entry criteria. * No presence of active renal condition (infection, requirement for dialysis or any other condition that could affect participant's safety). Participants with isolated proteinuria resulting from MM are eligible, provided they fulfill inclusion criteria. * No evidence of active mucosal or internal bleeding. * No known immediate or delayed hypersensitivity reaction or idiosyncratic reactions to belamaf or drugs chemically related to belamaf, or any of the components of the study treatment. * Symptomatic amyloidosis, active POEMS syndrome (polyneuropathy, organomegaly, endocrinopathy, monoclonal plasma proliferative disorder, skin changes) or active plasma cell leukemia at the time of screening. * Chronic concomitant treatment with strong inhibitors of CYP3A4 is not allowed on this study. Patients on strong CYP3A4 inhibitors must discontinue the drug for 14 days prior to registration on the study. Chronic concomitant treatment with strong CYP3A4 inducers is not allowed. Patients must discontinue the drug 14 days prior to the start of study treatment. Participant must not have current corneal epithelial disease except mild changes in corneal epithelium. For belantamab mafodotin, concomitant administration with strong inhibitors of OATP should be avoided. * RE-REGISTRATION ELIGIBILITY CRITERIA: Patients must meet criteria for progression of myeloma as defined by IMWG criteria indicated as any of the following: * ≥ 25% increase in M-protein (must be at least 0.5 g/dl above nadir from last treatment regimen). * 25% difference between involved and uninvolved serum free light chains from its nadir or * The development of new plasmacytomas or hypercalcemia not due to other causes. In the absence of progression by serum M protein or free light chain, biopsy of new plasmacytoma of extramedullary disease is warranted. * If refractory myeloma, it should be defined by IMWG criteria as disease which has become non-responsive or progressive on belamaf/dexamethasone. * RE-REGISTRATION ELIGIBILITY CRITERIA: Measurable disease defined by IMWG criteria as: * Serum M-protein ≥ 0.5 g/dL. * Urine monoclonal protein ≥ 200 mg/24h. * Serum FLC assay: Involved FLC level ≥ 10 mg/dl (≥ 100 mg/l) and serum free light chain ratio is abnormal. * PET/CT or MRI findings consistent with (c/w) disease progression. * RE-REGISTRATION ELIGIBILITY CRITERIA: Absolute neutrophil count (ANC) ≥ 1,000/mm\^3. * RE-REGISTRATION ELIGIBILITY CRITERIA: Platelet Count ≥ 75,000/mm\^3 (or ≥ 50,000/mm\^3 if BM plasma cells \> 50%). * RE-REGISTRATION ELIGIBILITY CRITERIA: Calc. creatinine clearance ≥ 30 mL/min using Cockcroft-Gault equation. * RE-REGISTRATION ELIGIBILITY CRITERIA: Total bilirubin ≤ 2 mg/dL. * RE-REGISTRATION ELIGIBILITY CRITERIA: AST/ALT ≤ 2.5 x upper limit of normal (ULN). * RE-REGISTRATION ELIGIBILITY CRITERIA: Alkaline phosphatase ≤ 3 x ULN.