Trial Studying Maintenance Treatment With Lenalidomide and Dexamethasone Versus Lenalidomide, Dexamethasone and MLN9708 After Autologous Hematopoietic Stem Cell Transplantation in Patients With Newly-diagnosed Symptomatic Multiple Myeloma

Inclusion Criteria: * The patient must, in the opinion of the investigator, be capable of complying with all requirements of the trial. * Have signed the informed consent form * Be between 18 and 67 years of age * Have an ECOG Performance Status \<= 2 (or 3 if the ECOG is due to myeloma, e.g. pathological fracture) * Multiple myeloma patient who was included in the GEM2012MENOS65 trial, and who is found to have, at a minimum, minimal response after consolidation * Life expectancy \> 3 months * The patient must have the following laboratory values in the 21 days prior to initiation of treatment (day 1, cycle 1): 1. Platelet count ≥ 100 x 109/L and absolute neutrophil count of ≥ 1.0 x 109/L. - Platelet transfusions to help patients meet eligibility criteria are not allowed. 2. Corrected serum calcium \< 14 mg/dL. 3. Aspartate transaminase (AST) and alanine transaminase (ALT) ≤ 2.5 x the upper limit of normal (ULN) 4. Total bilirubin within normal range 5. Calculated creatinine clearance \> 30 mL/min * Female patients who: 1. Are postmenopausal for at least 1 year before the screening visit, OR 2. Are surgically sterile, OR 3. If they are of childbearing potential, agree to practice 2 effective methods of contraception, at the same time, from the time of signing the informed consent form through 90 days after the last dose of study drug, AND 4. Must also adhere to the guidelines of any treatment-specific pregnancy prevention program, if applicable, OR 5. Agree to practice true abstinence when this is in line with the preferred and usual lifestyle of the subject. (Periodic abstinence \[eg, calendar, ovulation, symptothermal, post-ovulation methods\] and withdrawal are not acceptable methods of contraception.) * Male patients, even if surgically sterilized (ie, status post-vasectomy), must agree to one of the following: 1. Agree to practice effective barrier contraception during the entire study treatment period and through 90 days after the last dose of study drug, OR 2. Must also adhere to the guidelines of any treatment-specific pregnancy prevention program, if applicable, OR 30 Agree to practice true abstinence when this is in line with the preferred and usual lifestyle of the subject. (Periodic abstinence (eg, calendar, ovulation, symptothermal, post-ovulation methods\] and withdrawal are not acceptable methods of contraception.) Exclusion Criteria: * Patients not included in clinical trial GEM2012MENOS65 * Patients included in GEM2012MENOS65 who are not found to have a least minimal response after consolidation * Patients included in GEM2012MENOS65 who were discontinued prematurely due to toxicity or disease progression * Female patients who are lactating or have a positive serum pregnancy test during the screening period. * Central nervous system involvement * Infection requiring systemic antibiotic therapy or other serious infection within 14 days before study enrollment. * Systemic treatment, within 14 days before the first dose of MLN9708, with strong inhibitors of CYP1A2 (fluvoxamine, enoxacin, ciprofloxacin), strong inhibitors of CYP3A (clarithromycin, telithromycin, itraconazole, voriconazole, ketoconazole, nefazodone, posaconazole) or strong CYP3A inducers (rifampin, rifapentine, rifabutin, carbamazepine, phenytoin, phenobarbital), or use of Ginkgo biloba or St. John's wort. * Any serious medical or psychiatric illness that could, in the investigator's opinion, potentially interfere with the completion of treatment according to this protocol. * Known GI disease or GI procedure that could interfere with the oral absorption or tolerance of MLN9708 including difficulty swallowing. * Diagnosed or treated for another malignancy within 2 years before study enrollment or previously diagnosed with another malignancy and have any evidence of residual disease. Patients with nonmelanoma skin cancer or carcinoma in situ of any type are not excluded if they have undergone complete resection. * Peripheral neuropathy ≥ grade 2 in the 21 days prior to inclusion. * Known hypersensitivity to lenalidomide or to MLN9708, their analogues, or excipients in the various formulations of any agent. * Patients who have had a myocardial infarction in the six months prior to inclusion in the clinical trial, or who are class III or IV according to the New York Heart Association (NYHA), heart failure unstable angina, uncontrolled ventricular arrhythmias or acute ischemia detected by electrocardiogram, or conduction disorders. * Patients who are currently participating in another clinical trial or receiving any other investigational product. * Seropositive for HVB, HVC or HIV.