Carfilzomib and Stem Cell Transplant for Plasma Cell Myeloma

* INCLUSION CRITERIA: Multiple myeloma criteria for newly or recently diagnosed subjects * Presence of clonal plasma cells in the bone marrow greater than or equal to 10% or a documented clonal plasmacytoma (either by immuno-histochemistry or by Ig gene rearrangement), AND * Presence of an M-component; an M-component (immunoglobulin G (IgG) or immunoglobulin A (IgA)) in serum greater than or equal to 1g/dl or in urine greater or equal to 200 mg/24 h. ALTERNATIVELY, if the M-component criterion is not met: * An abnormal serum free light chain (FLC) ratio on the serum FLC assay, or if the FLC ratio is normal, * Baseline bone marrow must have 10% or greater clonal plasma cells AND, IN ADDITION, presence of one or more of the following attributable to the disease (in the presence or absence of an M-component): * Calcium elevation greater than 11.5 mg/dl (2.65 mmol/l) * Renal insufficiency: serum creatinine greater than 2 mg/dl (177 mmol/l) or less than 60ml/min. * Hemoglobin less than 10 g/dl (12.5 mmol/l) or 2 g/dl (1.25 mmol/l) below lower normal * Bone disease (lytic lesions or osteopenia) * Other evidence of disease activity: repeated infections, secondary amyloidosis, hyperviscosity, hypogammablobulinemia Criteria for subjects with persistent or recurrent disease Subjects with recurrent or persistent disease are eligible if: * Criteria for initiating therapy for plasma cell myeloma (PCM) had been present at the time of initiation of therapy or there is clear clinical indication for salvage therapy. * They have not undergone an autologous transplant for the treatment of PCM * They have received no more than two salvage regimens for the treatment of recurrent or persistent PCM (each regimen may include more than one cycle) Other eligibility criteria -Age \> 18 years and less than or equal to 75 years. In subjects between 65 and 75 years of age, physiologic age and co-morbidity will be thoroughly evaluated before enrolling. Specifically, any history of cardiovascular pathology or symptoms not clearly fitting the exclusion criteria of Section 2.1.2 will prompt an evaluation by a Clinical Center Cardiologist and eligibility will be considered on a case-by-case basis. * Karnofsky performance status of 70% or greater (Eastern Cooperative Oncology Group (ECOG) 0 or 1) * Ejection fraction (EF) by multi-gated acquisition scan (MUGA) or 2-D echocardiogram within institution normal limits. In case of low ejection fraction (EF), the subject may remain eligible after a stress echocardiogram is performed if the EF is more than 35% and if the increase in EF with stress is estimated at 10% or more. * creatinine clearance \> 25ml/min (measured on a 24 hour urine collection) * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) less than or equal to 3 x upper limit of normal * Bilirubin less than or equal to1.5 (except if due to Gilbert's disease) * Corrected carbon dioxide diffusing capacity (DLCO) greater than or equal to 40% on pulmonary function tests EXCLUSION CRITERIA: * Prior allogeneic or autologous stem cell transplantation * Prior treatment with Carfilzomib (CFZ) is not an exclusion * History of recent (\< 6 months) cerebrovascular accident * History of documented recent (\< 6 months) pulmonary embolus * Clinically significant cardiac pathology: * Myocardial infarction within 6 months prior to enrollment, * Class III or IV heart failure according to New York Heart Association (NYHA), * Uncontrolled angina, * Severe uncontrolled ventricular arrhythmias, or * Electrocardiographic evidence of acute ischemia or active conduction abnormalities felt to pose a significant cardiac riks by a Cardiology consultant * Patients with a history of coronary artery bypass grafting or angioplasty will receive a cardiology evaluation and be considered on a case-by-case basis. * Human immunodeficiency virus (HIV) seropositive * Acute active infection requiring treatment (systemic antibiotics, antivirals, or antifungals) within 14 days prior to enrollment * Active hepatitis B or C infection * Uncontrolled hypertension or uncontrolled diabetes within 14 days prior to enrollment * Major surgery within 21 days prior to enrollment * Non-hematologic 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 * Significant neuropathy (Grades 3 4, or Grade 2 with pain) within 14 days prior to randomization * Known history of allergy to Captisol (a cyclodextrin derivative used to solubilize CFZ) * Patients known or found to be pregnant * Female patients of childbearing age who are unwilling to practice contraception * Patients may be excluded at the discretion of the principal investigator (PI) if it is deemed that allowing participation would represent an unacceptable medical or psychiatric risk. * Patients must be able to give informed consent