Lenalidomide With or Without Ixazomib Citrate and Dexamethasone in Treating Patients With Residual Multiple Myeloma After Donor Stem Cell Transplant

Inclusion Criteria: * Patients who completed induction treatment followed by autologous stem cell transplant as initial therapy for symptomatic myeloma as per IMWG criteria and initiated Revlimid (lenalidomide) maintenance * Patients must have initiated lenalidomide maintenance at approximately 3 months post autologous stem transplant (preferably 70-90 but not more than 120 days) * Patients must be receiving lenalidomide 10 mg or 15 mg and be able to tolerate dose escalation to 25 mg daily * Patients must have received lenalidomide maintenance for 3 months (+1 month window for a maximum of 4 months lenalidomide prior to enrollment) * No evidence of progressive disease on lenalidomide * Any measurable residual disease at the time of screening for the study documented in at least one of the following ways: * Serum protein electrophoresis (SPEP)/immunofixation studies (IFIX) positive disease * Freelite only positive disease * SPEP/IFIX - negative and Freelite- negative but MRD-positive disease is allowed * Evidence of MRD at the time of screening for this study by multi-color flow cytometry (bone marrow procedure at screening required) * Bone marrow specimen will be required at study entry; available deoxyribonucleic acid (DNA) sample will be used for calibration step for MRD evaluation by gene sequencing * Life expectancy of more than 3 months * Eastern Cooperative Oncology Group (ECOG) performance status of 0-2 * Bilirubin =\<1.5 x upper limit of normal (ULN) * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 3 x ULN * Absolute neutrophil count (ANC) \>= 1.0 x 10\^9/L * Hemoglobin \>= 8 g/dL * Platelet count \>= 75 x 10\^9/L * Calculated creatinine clearance (by Cockroft-Gault) \>= 50 ml/min or serum creatinine below 2 g/dL * Voluntary written consent must be given before performance of any study related procedure not part of standard medical care, with the understanding that consent may be withdrawn by the patient at any time without prejudice to future medical care * Female patients who: * Are postmenopausal for at least 1 year before the screening visit, OR * Are surgically sterile, OR * If they are of childbearing potential, agree to practice 2 effective methods of contraception, at the same time, from the time of signing the informed consent form through 90 days after the last dose of study drug, OR * Agree to practice true abstinence when this is in line with the preferred and usual lifestyle of the subject; (periodic abstinence \[e.g., calendar, ovulation, symptothermal, post-ovulation methods\] and withdrawal are not acceptable methods of contraception) * Male patients, even if surgically sterilized (i.e., status post-vasectomy), must agree to one of the following: * Agree to practice effective barrier contraception during the entire study treatment period and through 90 days after the last dose of study drug, OR * Agree to practice true abstinence when this is in line with the preferred and usual lifestyle of the subject; (periodic abstinence \[e.g., calendar, ovulation, symptothermal, post-ovulation methods\] and withdrawal are not acceptable methods of contraception) Exclusion Criteria: * Evidence of progressive disease on lenalidomide maintenance as per IMWG criteria * Patients who have already started or received multi-drug consolidation regimen post-transplant expect for lenalidomide maintenance * Diarrhea \> grade 1 in the absence of anti-diarrheals * Central nervous system involvement * Female patients who are lactating or have a positive serum pregnancy test during the screening period * History of allergy to mannitol * Major surgery within 14 days before enrollment * Radiotherapy within 14 days before randomization; if the involved field is small, 7 days will be considered a sufficient interval between treatment and administration of the ixazomib * Evidence of current uncontrolled cardiovascular conditions, including uncontrolled cardiac conditions such as hypertension, or cardiac arrhythmias, or New York Heart Association stage III and IV congestive heart failure, or unstable angina or myocardial infarction within the past 6 months * Rate-corrected QT interval of electrocardiograph (QTc) \> 470 msec on a 12-lead electrocardiogram (ECG) during screening * Uncontrolled diabetes * Acute infection requiring systemic anti-infectives, antivirals, or antifungals within two weeks prior to first dose * Systemic treatment, within 14 days before the first dose of ixazomib, with strong inhibitors of cytochrome P450 family 3, subfamily A, polypeptide 2 (CYP1A2) (fluvoxamine, enoxacin, ciprofloxacin), strong inhibitors of cytochrome P450 family 3, subfamily A CYP3A (clarithromycin, telithromycin, itraconazole, voriconazole, ketoconazole, nefazodone, posaconazole) or strong CYP3A inducers (rifampin, rifapentine, rifabutin, carbamazepine, phenytoin, phenobarbital), or use of Ginkgo biloba or St. John's wort * Ongoing or active systemic infection, active hepatitis B or C virus infection, or known human immunodeficiency virus (HIV) positive * Any serious medical or psychiatric illness that could, in the investigator's opinion, potentially interfere with the completion of treatment according to this protocol * Known allergy to any of the study medications, their analogues, or excipients in the various formulations of any agent * Known gastrointestinal (GI) disease or GI procedure that could interfere with the oral absorption or tolerance of ixazomib including difficulty swallowing * Diagnosed or treated for another malignancy within 2 years before study enrollment or previously diagnosed with another malignancy and have any evidence of residual disease; patients with nonmelanoma skin cancer or carcinoma in situ of any type are not excluded if they have undergone complete resection * Patient has \>= grade 3 peripheral neuropathy, or grade 2 with pain on clinical examination during the screening period * Participation in other clinical trials, including those with other investigational agents not included in this trial, within 30 days of the start of this trial and throughout the duration of this trial