Dexamethasone, Elotuzumab, and Pomalidomide in Treating Patients With Refractory Multiple Myeloma

Inclusion Criteria: * Age \>= 18 years * Pathologically confirmed diagnosis of multiple myeloma and noted to have progressive disease (International Myeloma Working Group \[IMWG\] criteria). * At least one prior line of therapy. * Disease refractory to daratumumab as defined by disease progression while on or =\< 60 days of completing treatment with a daratumumab-containing regimen as part of any prior line of therapy. * Measurable disease =\< 14 days prior to registration. * Eastern Cooperative Oncology Group (ECOG) Performance Status (PS) 0, 1 or 2. * Absolute neutrophil count (ANC) \>= 1,000 cell/mm\^3 without growth factor support (obtained =\< 14 days prior to registration). * Platelet \>= 50,000 cells/mm\^3 for patients who have bone marrow plasmacytosis \< 50% or \>= 30,000 cells/mm\^3 for patients who have bone marrow plasmacytosis of \>= 50% (obtained =\< 14 days prior to registration). * Total bilirubin =\< 1.5 x upper limit of normal (ULN) unless due to Gilbert's syndrome, in which case the direct bilirubin must be =\< 1.5 x ULN (obtained =\< 14 days prior to registration). * Alanine aminotransferase (ALT) and aspartate transaminase (AST) =\< 3 x ULN (obtained =\< 14 days prior to registration). * Prothrombin time (PT)/international normalized ratio (INR)/activated partial thromboplastin time (aPTT) =\< 1.5 x ULN OR if patient is receiving anticoagulant therapy and PT/INR or aPTT is within target range of therapy (obtained =\< 14 days prior to registration). * Calculated or measured creatinine clearance \>= 30 ml/min (obtained =\< 14 days prior to registration). * Negative urine or serum pregnancy test done =\< 14 days prior to registration, for persons of childbearing potential only. * NOTE: If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required. * Provide written informed consent. * Willing to return to enrolling institution for follow-up (during the Active Monitoring Phase of the study). * Willing to follow the requirements of the (Revlimid/Pomalyst) Risk Evaluation and Mitigation Strategies (REMS) program. Exclusion Criteria: * Non-secretory multiple myeloma (MM) or known immunoglobulin light chain (AL) amyloidosis. * Clinically significant active infection requiring intravenous antibiotics (=\< 14 days prior to registration). * \>= Grade 3 neuropathy and/or POEMS syndrome (plasma cell dyscrasia with polyneuropathy, organomegaly, endocrinopathy, monoclonal protein, and skin changes). * Immunocompromised patients and patients known to be human immunodeficiency virus (HIV) positive and currently receiving antiretroviral therapy. * NOTE: Patients known to be HIV positive, but without clinical evidence of an immunocompromised state, are eligible for this trial. * Concurrent therapy considered investigational. * NOTE: Patients must not be planning to receive any radiation therapy (except localized radiation for palliative care that must be completed prior to starting Cycle 1, Day 1). * Any of the following because this study involves an investigational agent whose genotoxic, mutagenic and teratogenic effects on the developing fetus and newborn are unknown: * Pregnant women. * Nursing women (lactating females are eligible provided that they agree not to breast feed while taking lenalidomide). * Men or women of childbearing potential who are unwilling to employ adequate contraception. * Other active malignancy =\< 3 years prior to registration. * EXCEPTIONS: * Adequately treated basal cell or squamous cell skin cancer. * Any in situ cancer. * Adequately treated Stage I or II cancer from which the patient is currently in complete remission, or * NOTE: If there is a history of prior malignancy, they must not be receiving other specific treatment for their cancer. * Major surgery =\< 4 weeks prior to registration. * History of stroke/intracranial hemorrhage =\< 6 months prior to registration. * Clinically significant cardiac illness including New York Heart Association (NYHA) Class III or Class IV heart failure, unstable angina pectoris, myocardial infarction within the past 6 months, or \>= Grade 3 cardiac arrhythmias noted =\< 14 days prior to registration. * Currently active, clinically significant hepatic impairment Child-Pugh class B or C according to the Child Pugh classification. * Exhibiting clinical signs of meningeal involvement of multiple myeloma. * Known severe chronic obstructive pulmonary disease or asthma defined as forced expiratory volume (FEV1) in 1 second \< 60% of expected. * Prior exposure to elotuzumab. * Prior history of disease refractory to pomalidomide. * Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens. * Uncontrolled intercurrent illness including, but not limited to: * Ongoing or active infection. * Symptomatic congestive heart failure. * Unstable angina pectoris. * Cardiac arrhythmia. * Or psychiatric illness/social situations that would limit compliance with study requirements.