Busulfan, Melphalan, and Bortezomib Before First-Line Stem Cell Transplant in Treating Patients With Multiple Myeloma

Inclusion Criteria: * Patients must have histologically or cytologically confirmed multiple myeloma * Measurable disease must be present as defined by protein criteria (quantifiable M-component in serum, urine or serum free light chains) in order to evaluate response as per IMWG; non-secretory patients are eligible provided the patient has \> 20% plasmacytosis OR multiple (\> 3) focal plasmacytomas or focal lesions on magnetic resonance imaging (MRI) * Patients must have received induction chemotherapy for myeloma, but not more than 12 months of prior chemotherapy for this disease, and must be eligible for the first planned autologous transplant * A minimum stem cell dose of 2.0 x 10\^6 cluster of differentiation 34-positive (CD34+) cells/kg has been collected * Life expectancy of greater than 12 months * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%) * Leukocytes \>= 3,000/mcL (unless myeloma related) * Absolute neutrophil count \>= 1,500/mcL (unless myeloma related) * Platelets \>= 50,000/mcL (unless myeloma related) * Total bilirubin =\< 2 x institutional upper limit of normal unless 2nd to Gilbert's disease * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3 x institutional upper limit of normal * Creatinine =\< 1.5 x institutional upper limit of normal OR creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients …