Fractionated Stem Cell Infusions in Myeloma Patients Undergoing Autologous Stem Cell Transplant

Inclusion Criteria: * Age ≥18 and \< than or = to 75 * Histologic and serologic findings, reviewed at MSKCC, confirming the diagnosis of multiple myeloma. Standard diagnostic criteria for multiple myeloma will be used, as per the International Myeloma Foundation consensus guidelines (Durie et al, 2003) . * Patients must have symptomatic multiple myeloma who have responded to prior induction or salvage chemotherapy (i.e. chemosensitive disease): * Patients who are receiving high-dose melphalan and ASCT as part of their initial therapy require at least minor response to their last line of therapy to document chemosensitive disease (Anderson et al. 2008) * Patients who are receiving high-dose melphalan and ASCT as part of salvage therapy require at least a minor response to their last line of therapy to document chemosensitive disease (Anderson et al. 2008). * There is no limit on the number of prior regimens received by the patient. * Patients must have at least 7 x 10\^6 (+/- 0.5 x 10\^6) CD34+ stem cells/kg frozen if he/she is being treated as part of a salvage (second) transplant strategy; patients must have 10 x 10\^6 (+/- 0.5 x 10\^6) CD34+ stem cells/kg frozen if ASCT is being performed as part of initial therapy. * Adequate organ function is required, defined as follows: * Serum bilirubin ≤ 2.0 mg/dl * AST, ALT and alkaline phosphatase \< 3 times the upper limit of laboratory normal * Creatinine clearance \> or = to 40 ml/min (24 hour urine collection or calculated\*) \*To be calculated by the Cockroft-Gault method: (140-Age) x Mass (kg) x \[0.85 if female\] (72 x Creatinine (mg/dL) * LVEF \> or = to 45% by MUGA or rest ECHO * Diffusing capacity \> or = to 45% (adjusted for hemoglobin) predicted by pulmonary function testing * Performance status KPS \> or = to 70%. Exclusion Criteria: * Unstable angina or myocardial infarction within 4 months of initiating therapy on trial, NYHA Class III or IV heart failure, uncontrolled angina, severe uncontrolled ventricular arrhythmias, sick sinus syndrome, or electrocardiographic evidence of acute ischemia or Grade 3 conduction system abnormalities unless subject has a pacemaker * Pregnant or lactating females * Nonhematologic malignancy within the past 3 years with the exception of a) adequately treated basal cell carcinoma, squamous cell skin cancer, or thyroid cancer; b) carcinoma in situ of the cervix or breast; c) prostate cancer of Gleason Grade 6 or less with stable prostate-specific antigen levels; or d) cancer considered cured by surgical resection or unlikely to impact survival during the duration of the study, such as localized transitional cell carcinoma of the bladder or benign tumors of the adrenal or pancreas * Contraindication to melphalan or any of the required supportive treatments, including hypersensitivity to G-CSF or pegfilgrastim * Any other medical condition or laboratory evaluation that, in the treating physician's or principal investigator's opinion, makes the patient unsuitable to participate in this clinical trial