Phase II Study of V-BEAM Conditioning Regimen Prior to Second Autologous Stem Cell Transplantation

Inclusion Criteria: * Patient must have a histologically confirmed diagnosis of multiple myeloma. * Patient must have received a prior autologous stem cell transplantation with melphalan conditioning for multiple myeloma with subsequent disease progression and repeat autologous stem cell transplantation is deemed appropriate by the treating physicians. * Patient must receive induction chemotherapy including 2 to 4 cycles of anti-myeloma therapy including bortezomib, with or without immune modulating agents and/or corticosteroids, Completion of induction therapy will occur within 30 days of first study drug dose. * Patient must have ≥ 2x106/kg CD34+ autologous stem cells available for transplantation. * Patient must be ≥ 18 years of age. * Patient must have life expectancy of greater than 6 months. * Patient must have an ECOG performance status ≤ 2 or Karnofsky performance status ≥ 60% (see Appendices A and B) * Patient must have normal bone marrow and organ function as defined below within 14 days prior to first study drug dose (conditioning regimen): * Absolute neutrophil count ≥500/mm3 * Platelets ≥ 50,000/mm3 * Hemoglobin ≥ 8 g/dl * Total bilirubin ≤ 1.5 x IULN * AST(SGOT)/ALT(SGPT) ≤ 3.0 x IULN * Creatinine clearance (Appendix C) ≥30 mL/min/1.73m2 * Women of childbearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control, abstinence) prior to study entry through Day +100 visit. Should a woman become pregnant or suspect she is pregnant while participating in this study, she must inform her treating physician immediately. * Patient must be able to understand and willing to sign an IRB approved written informed consent document. Exclusion Criteria: * Patient must not be refractory to induction therapy. Refractory is defined as disease progression while on therapy or within 30 days following completion of therapy. * Patient must not have had disease progression requiring active treatment within 12 months of previous autologous stem cell transplant. Maintenance therapy is not considered active treatment. * Patient must not have peripheral neuropathy ≥ grade 3 based on NCI CTCAE v 4.0 (Appendix D). * Patient must not be receiving renal replacement therapy, hemodialysis, or peritoneal dialysis. * Patient must not have another concurrent malignancy requiring treatment. * Patient must not be receiving any other investigational agents within 14 days prior to the first dose of study drug. * Patient must not have known brain metastases. Patients with known brain metastases must be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events. * Patient must not have a history of allergic reactions attributed to compounds of similar chemical or biologic composition to bortezomib, carmustine, etoposide, cytarabine, and melphalan, or other agents used in the study. * Patient must not have an uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. * Patient must not be pregnant and/or breastfeeding. Inclusion of Women and Minorities -Both men and women and members of all races and ethnic groups are eligible for this trial.