Ixazomib With Cyclophosphamide and Dexamethasone in Patients With Previously Untreated Symptomatic Multiple Myeloma or Light Chain Amyloidosis

Inclusion Criteria: * PHASE I ONLY: * COHORT A: multiple myeloma * COHORT B: biopsy proven light chain amyloidosis with organ involvement requiring therapy * Calculated creatinine clearance (using Cockcroft-Gault equation) \>= 30 mL/min * Absolute neutrophil count (ANC) \>= 1000/mm\^3 * Platelet count \>= 75000/mm\^3 * Hemoglobin \>= 8.0 g/dL * Total bilirubin =\< 1.5 x upper limit of normal (ULN) * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 3 x ULN * COHORT B ONLY: alkaline phosphatase =\< 750 U/L * COHORT B ONLY: N-terminal pro b-type natriuretic peptide (NT-ProBNP) \< 7500 ng/dL * Prior therapy for the treatment of solitary plasmacytoma is permitted, but \> 14 days should have elapsed from the last day of radiation; NOTE: prior therapy with clarithromycin, dehydroepiandrosterone (DHEA), anakinra, pamidronate or zoledronic acid is permitted; any additional agents not listed must be approved by the principal investigator * 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 * COHORT B ONLY: serum immunoglobulin free light chain \>= 5 mg/dL AND abnormal serum immunoglobulin kappa to lambda free light chain ratio * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1 or 2 * Previously untreated * Provide informed written consent * Negative pregnancy test done =\< 7 days prior to registration, for women of childbearing potential only * Willing to follow strict birth control measures as suggested by the study * Female patients: if they are of childbearing potential, agree to one of the following: * 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, AND must also adhere to the guidelines of any treatment-specific pregnancy prevention program, if applicable, OR * Agree to practice true abstinence when this is in line with the preferred and usual lifestyle of the subject (periodic abstinence \[eg, calendar, ovulation, symptothermal, post-ovulation methods\] and withdrawal are not acceptable methods of contraception) * Male patients: even if surgically sterilized (ie, 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 * Must also adhere to the guidelines of any treatment-specific pregnancy prevention program, if applicable, OR * Agree to practice true abstinence when this is in line with the preferred and usual lifestyle of the subject (periodic abstinence \[eg, calendar, ovulation, symptothermal, post-ovulation methods\] and withdrawal are not acceptable methods of contraception) * Willing to return to return to enrolling institution for follow-up (during the active monitoring phase of the study) Exclusion Criteria: * Monoclonal gammopathy of undetermined significance (MGUS) or smoldering myeloma only * Prior cytotoxic chemotherapy or corticosteroids for the treatment of multiple myeloma; NOTE: prior corticosteroid use for the treatment of non-malignant disorders is permitted * Diagnosed or treated for another malignancy =\< 2 years before study enrollment or previously diagnosed with another malignancy and have any evidence of residual disease; NOTE: 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 * Nursing women * Men or women of childbearing potential who are unwilling to employ adequate contraception * 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, 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 * Peripheral neuropathy \>= grade 3 on clinical examination or grade 2 with pain during the screening period * Major surgery =\< 14 days prior to study registration * Systemic treatment with strong CYP3A4 inducers (rifampin, rifapentine, rifabutin, carbamazepine, phenytoin, phenobarbital, Gingko biloba, St. John?s wort) =\< 14 days prior to registration * Evidence of current uncontrolled cardiovascular conditions (New York Heart Association \[NYHA\] class III or IV), including hypertension, cardiac arrhythmias, congestive heart failure, unstable 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 * Radiotherapy =\< 14 days prior to registration; NOTE: if the involved field is small, 7 days will be considered a sufficient interval between treatment and administration of the ixazomib * 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 * Participation in clinical trials with other investigational agents not included in this trial, =\< 30 days prior to registration