Bortezomib, Melphalan, and Total-Body Irradiation Before Stem Cell Transplant in Treating Patients With Multiple Myeloma

Inclusion Criteria: * Serum creatinine =\< 2 mg/dL * Serum total bilirubin =\< 1.5 X upper limit of normal (ULN) * Platelet count \>= 30,000/μL * Hemoglobin \>= 8.0 g/dL * Diagnosis of myeloma for which autologous stem cell transplant is being considered * Measurable disease of multiple myeloma at the time of baseline values for disease assessment 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 * Bone marrow plasma cells \>= 30% * NOTE: * For patients with no relapse prior to transplant, measurable disease at the time of diagnosis * For patients who have had a disease relapse prior to transplant, measurable disease at the time of the most recent relapse immediately prior to transplant. * If the patient had treatment for the relapsed disease prior to transplant, the patient must have measurable disease at the time of relapse prior to this therapy * Patient is considered for autologous stem cell transplantation with full dose melphalan (200 mg/m\^2) * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1 or 2 * Recovered from non-hematological toxicity of previous chemotherapy (excludes grade 1 neurotoxicity) * Voluntary written informed consent before performance of any study-related procedure not part of norm…