Carfilzomib, Lenalidomide, and Dexamethasone Before and After Stem Cell Transplant in Treating Patients With Newly Diagnosed Multiple Myeloma

Inclusion Criteria: * Newly diagnosed, myeloma requiring systemic chemotherapy as per International Myeloma Working Group (IMWG) uniform criteria: * Prior treatment of hypercalcemia or spinal cord compression or active and/or aggressively progressing myeloma with corticosteroids or lenalidomide or bortezomib-based regimens does not disqualify the patient (the treatment dose should not exceed the equivalent of 160 mg of dexamethasone in a 4 week period or not more than 1 cycle) * Bisphosphonates are permitted * Suitable and interested to proceed to ASCT * Measurable disease, prior to initial treatment as indicated by one or more of the following: * Serum monoclonal (M)-protein \>= 0.5 g/dL * Urine M-protein \>= 200 mg/24 hours * If serum protein electrophoresis is felt to be unreliable for routine M-protein measurement, then quantitative immunoglobulin levels are acceptable * Life expectancy of more than 3 months * Eastern Cooperative Oncology Group (ECOG) performance status 0-2 * Bilirubin \< 1.5 times the upper limit of normal (ULN) * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) \< 2.5 times ULN * Absolute neutrophil count (ANC) \>= 1.0 x 10\^9/L * Hemoglobin \>= 8 g/dL * Platelet count \>= 75 x 10\^9/L; subjects may receive red blood cell (RBC) transfusions or platelet transfusions, if clinically indicated in accordance with institutional guidelines; however, screening platelet count should be independent of platelet transfusions for at least 2 weeks * Calculated or measured creatinine clearance of \>= 50 mL/minute, calculated using the formula of Cockcroft and Gault * Written informed consent in accordance with federal, local, and institutional guidelines * Females of childbearing potential (FCBP) (defined as sexually mature females who: have not undergone a hysterectomy or bilateral oophorectomy; or have not been naturally postmenopausal for at least 24 consecutive months \[ie, has had menses at any time in the preceding 24 consecutive months\]) must agree to ongoing pregnancy testing * FCBP must have 2 negative pregnancy tests (sensitivity of at least 50 mIU/mL) prior to initiating lenalidomide; the first pregnancy test must be performed within 10-14 days before day 1 cycle 1 and the second pregnancy test must be performed within 24 hours of day 1 cycle 1; the subject may not receive lenalidomide until the treating investigator has verified that the results of these pregnancy tests are negative, and must agree to ongoing pregnancy tests as outlined in the protocol * FCBP must agree to use 2 reliable forms of contraception simultaneously or to practice complete abstinence from heterosexual intercourse during the following time periods related to this study: * For at least 28 days before starting lenalidomide * While participating in the study; and * For at least 28 days after discontinuation from the study; the 2 methods of reliable contraception must include a highly effective method (ie, intrauterine device (IUD), hormonal \[birth control pills, injections, or implants\], tubal ligation, partner's vasectomy) and an additional effective (barrier) method (ie, latex condom, diaphragm, cervical cap); FCBP must be referred to a qualified provider of contraceptive methods if needed * Male subjects must agree to use a latex condom during sexual contact with females of childbearing potential while participating in the study and for at least 28 days following discontinuation from the study even if he has undergone a successful vasectomy * Male subjects must agree to inform his physician if he has had unprotected sexual contact with a female who can become pregnant or if he thinks for any reason that his sexual partner may be pregnant * Male subjects must agree not to donate semen or sperm while taking lenalidomide * All study participants must be registered into the mandatory Rev Assist program and be willing and able to comply with the requirements of Rev Assist * The ability to take aspirin or other appropriate venous thromboembolism (VTE) prophylaxis * Subjects must agree to adhere to all study requirements, including birth control measures and pregnancy testing, visit schedule, outpatient treatment, required concomitant medications, and laboratory monitoring Exclusion Criteria: * Non-secretory or hyposecretory multiple myeloma, prior to initial treatment defined as \< 0.5 g/dL M-protein in serum, \< 200 mg/24 hr urine M-protein, or disease only measured by serum free light chain * POEMS syndrome (polyneuropathy, organomegaly, endocrinopathy, monoclonal protein, and skin changes) * Waldenstrom's macroglobulinemia or immunoglobin (Ig)M myeloma * Radiotherapy to multiple sites or immunotherapy within 4 weeks before start of protocol treatment (localized radiotherapy to a single site at least 1 week before start is permissible) * Participation in an investigational therapeutic study within 3 weeks or within 5 drug half-lives (t1/2) prior to first dose, whichever time is greater * Pregnant or lactating females * History of allergy to mannitol * Major surgery within 3 weeks prior to first dose * Myocardial infarction within 6 months prior to enrollment, New York Heart Association (NYHA) class III or IV heart failure, uncontrolled angina, severe uncontrolled ventricular arrhythmias, or electrocardiographic evidence of acute ischemia or active conduction system abnormalities * Uncontrolled hypertension or diabetes * Acute active infection requiring systemic antibiotics, antivirals, or antifungals within two weeks prior to first dose * Known or suspected human immunodeficiency virus (HIV) infection, known HIV seropositivity * Active hepatitis A, B, or C infection * Non-hematologic malignancy within the past 3 years except adequately treated basal cell, squamous cell skin cancer, thyroid cancer, carcinoma in situ of the cervix, or prostate cancer \< Gleason grade 6 with stable prostate specific antigen levels or cancer considered cured by surgical resection alone * Any clinically significant medical disease or condition that, in the investigator's opinion, may interfere with protocol adherence or a subject's ability to give informed consent * Significant neuropathy (grades 3-4, or grade 2 with pain) at the time of the first dose and/or within 14 days before enrollment * Contraindication to any of the required concomitant drugs, including proton-pump inhibitor (eg, lansoprazole), enteric-coated aspirin, allopurinol or if a history of prior thrombotic disease, warfarin or low molecular weight heparin * Subjects in whom the required program of PO and IV fluid hydration is contraindicated, eg, due to pre-existing pulmonary, cardiac, or renal impairment * Subjects with known or suspected amyloidosis of any organ * Subjects with pleural effusions requiring thoracentesis or ascites requiring paracentesis * No coverage or not-acceptable by patient co-pay for lenalidomide