Bortezomib Followed by High-Dose Melphalan and Bortezomib as Conditioning Regimen for Tandem Stem Cell Transplants

Inclusion Criteria: * Voluntary written informed consent before performance of any study-related procedure not part of normal medical care, with the understanding that consent may be withdrawn by the subject at any time without prejudice to future medical care. * Female is either post-menopausal or surgically sterilized or willing to use an acceptable method of birth control (i.e., a hormonal contraceptive, intra-uterine device, diaphragm with spermicide, condom with spermicide, or abstinence) for the duration of the study. * Male agrees to use an acceptable method for contraception for the duration of the study. * Multiple Myeloma Criteria: * Patients with primary refractory disease (those failing to achieve at least a partial response, as defined by the Bladé multiple myeloma response criteria, after first-line (induction) therapy). A partial response will be defined as the following: ≥50% reduction in the level of the serum monoclonal paraprotein, maintained for a minimum of 6 weeks, Reduction in 24-hour urinary light chain excretion either by ≥ 90% or to \< 200 mg, maintained for a minimum of 6 weeks. For patients with non-secretory myeloma only, ≥ 50% reduction in plasma cells in a bone marrow aspirate and biopsy, maintained for a minimum of 6 weeks, ≥ 50% reduction in the size of soft tissue plasmacytomas (by radiography or physical examination). No increase in the size or number of lytic bone lesions (development of a compression fracture does not exclude response). * Patients with plasma cell leukemia, either newly diagnosed or previously treated. * Patients greater than or equal to 18 years of age are eligible. * Patients must have a histologically confirmed diagnosis by a pathologic review at the H. Lee Moffitt Cancer Center and Research Institute. * Patients must have undergone a complete psychosocial evaluation and have been considered capable of compliance. Exclusion Criteria: * Patient has a platelet count of \<30× 10\^9/L within 14 days before enrollment. * Patient has an absolute neutrophil count of \<1.0 × 10\^9/L within 14 days before enrollment. * Patient has a serum creatinine of greater than 2.0 mg/dL OR a creatinine clearance of less than 40 ml/minute within 14 days before enrollment. Creatinine clearance can be measured or calculated. * Has \>Grade 2 peripheral neuropathy within 14 days before enrollment. * Myocardial infarction within 6 months prior to enrollment or has New York Hospital Association (NYHA) Class III or IV heart failure (see section 8.4), 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 has to be documented by the investigator as not medically relevant. * Patient has hypersensitivity to bortezomib, boron or mannitol. * Female is pregnant or breast-feeding. Confirmation that the subject is not pregnant must be established by a negative serum β-human chorionic gonadotropin (β-hCG) pregnancy test result obtained during screening. Pregnancy testing is not required for postmenopausal or surgically sterilized women. * Patient has received other investigational drugs with 14 days before enrollment * Serious medical or psychiatric illness likely to interfere with participation in this clinical study. * Patients with a DLCO less than 50% (adjusted) of normal or with symptomatic obstructive or restrictive lung disease are ineligible. * Patients with renal dysfunction secondary to multiple myeloma may be enrolled at the discretion of the principal investigator. However, patients on hemodialysis or peritoneal dialysis are ineligible. * Patients with a total bilirubin greater than 2.0 mg/dL and SGOT or SGPT greater than two and a half times normal (unless due to primary malignancy), or a history of severe hepatic dysfunction are ineligible. * Patients with active infections are ineligible. * Patients who are HIV positive are ineligible. * Patients with active leptomeningeal involvement are ineligible. Patients with a history of previous CSF tumor involvement without symptoms or signs are eligible provided the CSF is now free of disease on lumbar puncture, and MRI of the brain shows no tumor involvement. Patients with severe symptomatic central nervous system (CNS) disease of any etiology are ineligible. * Patients with uncontrolled insulin-dependent diabetes mellitus or uncompensated major thyroid or adrenal dysfunction are ineligible. * Patients with an Eastern Cooperative Oncology Group (ECOG) performance status of ≥ 2 are ineligible. * Patients with an ECOG performance status of 2 to 3, secondary to bone pain, may be enrolled at the discretion of the institutional investigator(s).