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 statu…