Phase I: Melphalan, Bendamustine and Carfilzomib for Autologous Transplant in Multiple Myeloma

Inclusion Criteria: * Diagnosis of multiple myeloma * At least 2 x 106 CD34+ cells/kg have been collected from the patient and cryopreserved for ASCT * Greater than 18 years * Karnofsky score greater than 70% * No evidence of progressive bacterial, viral, or fungal infection * Absolute neutrophil count above 1000 * Platelet count above 50,000 * Hemoglobin above 8 g/dL * Creatinine clearance greater than 50 mL/min * Total bilirubin, ALT, and AST less than 2 x the upper limit of normal * Alkaline phosphatase less than or equal to 250 IU/L * Left Ventricular Ejection Fraction (LVEF) greater than or equal to 45% * Adjusted Carbon Monoxide Diffusing Capacity (DLCO) greater than or equal to 60% * Negative HIV serology * Recovered from toxicity of previous chemotherapy (excludes grade 1 neurotoxicity and hematological toxicity) * Patients with a pre-transplant disease status consistent with a very good partial response (VGPR), partial response (PR), stable disease (SD), progressive disease (PD), or relapse from complete remission (CR). Exclusion Criteria: * Patients who are refractory to carfilzomib. Refractory is defined as disease progression while on carfilzomib therapy after receiving at least two cycles of treatment. * Patients with a complete response (CR) (including near CR and stringent CR) to conventional induction therapy and proceeding to transplantation. * Pregnant or nursing females or women of reproductive capability who are unwilling to use effective contraception. A woman of reproductive capability is one who has not undergone a hysterectomy (removal of the womb), has not had both ovaries removed, or has not been post-menopausal (stopped menstrual periods) for more than 24 months in a row. * Male subjects who refuse to practice effective barrier contraception during the entire study treatment period and through a minimum of 30 days after the last dose of study drug, or completely abstain from heterosexual intercourse. This must be done even if they are surgically sterilized (ie, post-vasectomy). * Patient with Grade 2 peripheral neuropathy * Inability to provide informed consent * Patient had myocardial infarction within 6 months prior to enrollment or has New York Heart Association (NYHA) Class III or IV heart failure, uncontrolled angina, severe uncontrolled ventricular arrhythmias, or electrocardiographic evidence of acute ischemia or active conduction system abnormalities. * Prior to study entry, any ECG abnormality at screening must be documented by the investigator as not medically relevant. * Known allergies to any of the components of the investigational treatment regimen or required ancillary treatments. * Serious medical or psychiatric illness likely to interfere with participation in this clinical study. * Diagnosed or treated for another malignancy within 3 years of enrollment (with the exception of non-melanoma skin cancer). * Participation in clinical trials with other investigational agents not included in this trial, within 14 days of the start of this trial and throughout the duration of this trial. * Prisoner