New drug combo shows promise for returning bone marrow cancer

Copied word for word from the study's registry entry, so the wording is the study team's rather than ours.

Inclusion Criteria: * Calculated creatinine clearance (using Cockcroft-Gault equation) \>= 30 mL/min (obtained =\< 14 days prior to registration) * Absolute neutrophil count \>= 1000/mL (obtained =\< 14 days prior to registration) * Untransfused platelet count \>= 75000/mL (obtained =\< 14 days prior to registration) * Hemoglobin \>= 8.0 g/dL (obtained =\< 14 days prior to registration) * Total bilirubin =\< 1.5 x the upper limit of the normal range (ULN) (obtained =\< 14 days prior to registration) * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 3 x ULN (obtained =\< 14 days prior to registration) * Patients with relapsed multiple myeloma who have already received one or more standard treatment regimens * Measurable disease of multiple myeloma as defined by at least ONE of the following: * Serum monoclonal protein \>= 1.0 g/dL * \>= 200 mg of monoclonal protein in the urine on 24 hour electrophoresis * Serum immunoglobulin free light chain \>= 10 mg/dL AND abnormal serum immunoglobulin kappa to lambda free light chain ratio * For patients with extramedullary disease (EMD) measurable disease by computed tomography (CT) or magnetic resonance imaging (MRI) or the CT portion of the positron emission tomography (PET)/CT: Must have at least one lesion that has a single diameter of \>= 2 cm. Skin lesions can be used if the area is \>= 2 cm in at least one diameter and measured with a ruler * Plasma cell count \>= 0.5 x 10\^9/L or 5 percent of the peripheral blood white cells * Plasma cell count if determined by flow cytometry, \>= 200/150,000 events * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1, 2 * Provide informed written consent * Negative pregnancy test done =\< 7 days prior to registration, for women of childbearing potential only * Willing to return to consenting Mayo Clinic institution for follow-up during the Active Monitoring Phase of the study; Note: during the Active Monitoring Phase of a study (i.e., active treatment and observation), participants must be willing to return to the consenting institution for follow-up * Recovered (i.e., \< grade 1 toxicity) from the reversible effects of prior antineoplastic therapy * Arms A - D only: Patients should be proteasome inhibitor naive (including bortezomib and carfilzomib) OR have received less than 6 cycles of therapy with a bortezomib or carfilzomib containing regimen and were not refractory to the bortezomib or carfilzomib based regimen (less than a PR or progression on or within 60 days of discontinuation) * Arm E only: Negative hepatitis B test (defined by a negative test for hepatitis B surface antigen \[HBsAg\], or antibodies to hepatitis B surface and/or core antigens \[antiHBs or antiHBc\]) (added as of addendum 9); Note: patients with serologic findings suggestive of hepatitis B virus (HBV) vaccination (antiHBs positivity as the only serologic marker) AND a known history of prior HBV vaccination do not need to be tested for HBV deoxyribonucleic acid (DNA) by polymerase chain reaction (PCR); those who are PCR positive will be excluded Exclusion Criteria: * Recent prior chemotherapy: * Alkylators (e.g. melphalan, cyclophosphamide) =\< 14 days prior to registration * Anthracyclines =\< 14 days prior to registration * High dose corticosteroids, immune modulatory drugs (thalidomide or lenalidomide) =\< 7 days prior to registration * Prior therapy with any proteasome inhibitor other than bortezomib, carfilzomib, or ixazomib * Concomitant high dose corticosteroids other than what is part of treatment protocol (concurrent use of corticosteroids); EXCEPTION: patients may be on chronic steroids (maximum dose 20 mg/day prednisone equivalent) if they are being given for disorders other than myeloma, i.e., adrenal insufficiency, rheumatoid arthritis, etc * 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 * Any of the following: * Pregnant women or women of reproductive ability who are unwilling to use 2 effective methods of contraception from the time of signing the informed consent form through 90 days after the last dose of study drug * Nursing women * Men who are unwilling to use a condom (even if they have undergone a prior vasectomy) while having intercourse with any woman, while taking the drug and for 30 days after stopping treatment * Other co-morbidity which would interfere with patient's ability to participate in trial, e.g. uncontrolled infection, uncompensated heart or lung disease * Other concurrent chemotherapy, radiotherapy, or any ancillary therapy considered investigational; NOTE: bisphosphonates are considered to be supportive care rather than therapy, and are thus allowed while on protocol treatment * Patient has \>= grade 3 peripheral neuropathy, or grade 2 with pain on clinical examination during the screening period * Major surgery within 14 days before study registration * Systemic treatment with strong inhibitors of cytochrome P450, family 1, subfamily A (CYP3A) inducers (rifampin, rifapentine, rifabutin, carbamazepine, phenytoin, phenobarbital), or use of Ginkgo biloba or St. John's wort within 14 days before the first dose of study treatment * Evidence of current uncontrolled cardiovascular conditions, including cardiac arrhythmias, congestive heart failure, angina, or myocardial infarction within the past 6 months; Note: prior to study entry, any electrocardiogram (ECG) abnormality at screening must be documented by the investigator as not medically relevant * Known human immunodeficiency virus (HIV) positive * Known hepatitis B surface antigen-positive status, or known or suspected active hepatitis C infection * 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 * Known gastrointestinal (GI) disease or GI procedure that could interfere with the oral absorption or tolerance of ixazomib including difficulty swallowing * Diarrhea \> grade 1, based on the National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE) grading, in the absence of antidiarrheals * Arm E only: Refractory to any combination of a proteasome inhibitor and daratumumab * Arm E only: Known chronic obstructive pulmonary disease with a forced expiratory volume in 1 second (FEV1) \< 50% of predicted normal. (Note that FEV1 testing is required for subjects suspected of having chronic obstructive pulmonary disease and subjects must be excluded if FEV1 \< 50% of predicted normal.) * Arm E only: Known moderate or severe persistent asthma within the past 2 years or currently has uncontrolled asthma of any classification