Ixazomib with Pomalidomide, Clarithromycin and Dexamethasone in Treating Patients with Multiple Myeloma

Inclusion Criteria: * Voluntary written consent * Patients must have a confirmed biopsy diagnosis of a multiple myeloma * Submission of original biopsy for review and verification by hematopathologist at local institution * Patients must have measurable disease according to International Myeloma Working Group (IMWG) criteria; measurable disease includes at least one of the following criteria: * Serum M-protein \>= 1.0 g/dL, and/or * Urine M-protein \>= 200 mg/24 hours, and/or * Involved serum free light chain \>= 10 mg/dL (\>= 100 mg/L) AND an abnormal serum free light chain ratio, and/or * Baseline marrow burden or myeloma of at least 30% * Disease that has progressed during or within 6 months of coming off therapy with bortezomib and lenalidomide (either sequentially or concurrent); progressive disease is defined as any of the following: * An increase of \>= 25% from lowest response value in any of the following: * Serum M-protein (absolute increase must be \>= 0.5 g/dL) AND/OR * Urine M-protein (absolute increase must be \>= 200 mg/24 hours) AND/OR * For patients without a measurable serum or urine M-protein but measurable disease by serum free light chain testing: Difference between the involved and uninvolved serum free light chain level (absolute increase must be \>= 10 mg/dL) AND/OR * For patients without a measurable serum or urine M-component or serum free light chain level: % marrow involvement with myeloma (absolute increase must be \>= 10%) AND/OR * Definite development of new bone lesions or extramedullary plasmacytomas or definite increase in the size of existing bone lesions or extramedullary plasmacytomas AND/OR * Hypercalcemia (corrected serum calcium \> 11.5 mg/dL) attributable to myeloma (e.g. not due to omitted doses of bisphosphonate) * Life expectancy of greater than 3 months * Eastern Cooperative Oncology Group (ECOG) performance status and/or other performance status 0, 1, or 2 * Disease free of prior malignancies for \> 5 years with exception of patients with nonmelanoma skin cancer or carcinoma in situ of any type are not excluded if they have undergone complete resection * Absolute neutrophil count (ANC) \>= 1,000/mm\^3 and * Platelet count \>= 50,000/mm\^3; note: platelet transfusions to help patients meet eligibility criteria are not allowed within 3 days before study enrollment * Total bilirubin =\< 2.0 × the upper limit of the normal range (ULN) * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 2.5 × ULN * Calculated creatinine clearance \>= 30 mL/min * 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 two 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: * Female patients who are lactating or have a positive serum pregnancy test during the screening period * Treatment with clarithromycin, anti-myeloma therapy including investigational agents or plasmapheresis within 30 days prior to treatment in this study * Failure to have fully recovered (i.e., =\< grade 1 toxicity or to patient's clinical baseline) from the reversible effects of prior chemotherapy * Major surgery within 14 days before enrollment * Radiotherapy within 14 days before enrollment * Central nervous system involvement * Infection requiring systemic antibiotic therapy or other serious infection within 14 days before study enrollment * Evidence of current uncontrolled cardiovascular conditions, including uncontrolled hypertension, uncontrolled cardiac arrhythmias, symptomatic congestive heart failure, unstable angina, or myocardial infarction within the past 6 months * Systemic treatment within 14 days before the first dose of study drugs, or concurrent use, with any of the following: * Strong inhibitors of cytochrome P450, family 1, subfamily A, polypeptide 2 (CYP1A2) * Strong inhibitors of family cytochrome P450 family 3, subfamily A (3A) * Strong cytochrome 3A polypeptide 4 inducers * Known ongoing or active systemic infection, active hepatitis B or C virus infection * Patients with human immunodeficiency virus (HIV) infection may be eligible provided they meet the following: * No history of acquired immunodeficiency syndrome (AIDS)-defining conditions or other HIV related illness * Cluster of differentiation (CD)4+ cells nadirs \> 350/mm\^3 * Treatment sensitive HIV and, if on anti-HIV therapy, HIV viral load \< 50 copies/mm\^3; please note: HIV+ patients who enroll on this study may need to modify their anti-retroviral therapy prior to receiving protocol therapy if they are on strong inducers or potent inhibitors of cytochrome P450; adverse events in HIV+ patients will be reported separately * 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 * Previous allergic reaction to an immunomodulatory drug (IMiD) * Known gastrointestinal (GI) disease or GI procedure that could interfere with the oral absorption or tolerance of study drugs including difficulty swallowing * Patient has \>= grade 3 peripheral neuropathy, or grade 2 with pain on clinical examination during the screening period * Previous treatment with ixazomib or pomalidomide