Immunomodulatory Drugs (Lenalidomide With or Without Pomalidomide) in Combination With a Corticosteroid Drug (Dexamethasone) for the Treatment of Multiple Myeloma

Inclusion Criteria: * Age \>= 18 years * COHORT A: Patient must have untreated smoldering multiple myeloma which is defined by the presence of 10% or more but less than 60% clonal plasma cells in the bone marrow and the absence of any of the following myeloma related symptoms or laboratory and radiographic abnormalities: anemia, hypercalcemia, renal insufficiency, hypercalcemia, serum free light chain ratio of greater than 100 or more than one focal marrow multiple myeloma lesion on magnetic resonance imaging (MRI) * COHORT B: Patient must have newly diagnosed myeloma requiring treatment and no prior therapies * COHORT C: Patient must have relapsed or refractory multiple myeloma with at least one prior therapy for their multiple myeloma but not refractory to all IMiDs * COHORT D: Patient must have relapsed or refractory multiple myeloma with lenalidomide as part of a maintenance regimen as their most recent therapy * Measurable disease * Provide written informed consent * Patient must be considered for treatment with an IMiD containing regimen * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1, 2 or 3 * Hemoglobin \>= 9.0 g/dL (obtained =\< 14 days prior to registration) * Absolute neutrophil count (ANC) \>= 1500/mm\^3 (obtained =\< 14 days prior to registration) * Platelet count \>= 100,000/mm\^3 (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 (=\< 5 x ULN for patients with liver involvement) (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 INR or aPTT is within target range of therapy (obtained =\< 14 days prior to registration) * Calculated creatinine clearance \>= 45 ml/min using the Cockcroft-Gault formula (obtained =\< 14 days prior to registration) * Negative pregnancy test done =\< 7 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 * Willing to return to enrolling institution for follow-up (during the Active Monitoring Phase of the study) * Willingness to provide mandatory blood and bone marrow specimens for correlative research * Willing to follow the requirements of the Pomalyst Risk Evaluation and Mitigation Strategy (REMS) program Exclusion Criteria: * An agent that has known genotoxic, mutagenic and teratogenic effects: * Pregnant persons * Nursing persons * Persons of childbearing potential who are unwilling to employ adequate contraception * 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 * Immunocompromised patients and patients known to be human immunodeficiency virus (HIV) positive and currently receiving antiretroviral therapy * 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 * Receiving any other investigational agent which would be considered as a treatment for the primary neoplasm * History of myocardial infarction =\< 6 months