Carfilzomib and Melphalan Before Stem Cell Transplant in Treating Patients With Multiple Myeloma

Inclusion Criteria: * Serum creatinine =\< 2 mg/dL * Absolute neutrophil count \>= 1000/uL * Platelet count \>= 50,000/uL * Hemoglobin \>= 8.0 g/dL * Diagnosis of symptomatic MM * 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 * NOTE: 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; NOTE: 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 toxicity of previous chemotherapy (excludes grade 1 neurotoxicity and hematological toxicity) * Provide informed written consent * Ejection fraction \>= 45% * Corrected pulmonary diffusion capacity of greater than or equal to 50% * Forced expiratory volume in 1…