Study of Captisol Enabled Melphalan and Pharmacokinetics for Patients With Multiple Myeloma or Light Chain Amyloidosis That Are Receiving an Autologous Transplant.

Inclusion Criteria: * Age ≥18 and ≤ 75 * Patients must have either: * Symptomatic multiple myeloma who have responded to prior induction or salvage chemotherapy (i.e. chemosensitive disease): Patients who are receiving high-dose melphalan and AHCT as part of their initial therapy require at least a partial response (PR) as defined by the International Myeloma Working Group uniform response criteria for MM. Patients who are receiving high-dose melphalan and AHCT as part of salvage therapy require at least a minor response to their last line of therapy to document chemosensitive disease. There is no limit on the number of prior regimens received by the patient. OR * Light chain (AL) amyloidosis who may be newly diagnosed or previously treated * Histologic and serologic findings, reviewed at MSKCC, confirming the diagnosis of multiple myeloma or AL amyloidosis. Standard diagnostic criteria for multiple myeloma will be used, as per the International Myeloma Foundation consensus guidelines * Patients must have at least 3 x 10\^6 CD34+ cells/kg frozen. * 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 ≥ 40 ml/min (24 hour urine collection) * LVEF ≥ 45% by MUGA or rest ECHO * Diffusing capacity ≥ 45% (adjusted for hemoglobin) predicted by pulmonary function testing * Performance status (ECOG) ≤ 2 * A willingness to avoid pregnancy or fathering children in male and female subjects respectively * A woman of childbearing potential must have a negative serum pregnancy test (β-human chorionic gonadotropin \[β-hCG\]) at screening and must be willing to avoid pregnancy during the study treatment period and for a specified duration (1 year post HCT) after the end of treatment. * Women of childbearing potential who have a negative serum pregnancy test at screening must practice a highly effective method of birth control (with at least 99% certainty) from screening through safety follow-up. Permitted methods that are at least 99% effective in preventing pregnancy should be communicated to the subject and their understanding confirmed. * Men who are enrolled must agree to take appropriate precautions to avoid fathering children (with at least 99% certainty) from screening through safety follow-up. Permitted methods that are at least 99% effective in preventing pregnancy should be communicated to the subject and their understanding confirmed 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 * Light chain (AL) amyloidosis patients with Mayo Cardiac Stage IIIB (defined as NT-proBNP\>8500 ng/L and Cardiac troponin (cTnT) \>0.035 μg/L) * 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 CE 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 * Any known allergy or allergic reactions to Captisol