Inclusion Criteria:

        KEY POINTS:

          1. Symptomatic multiple myeloma or asymptomatic myeloma with myeloma-related organ damage
             diagnosed according to standard criteria in patients who received allogeneic
             transplant due to high-risk prognostic features, such as, but not limited to:

               -  Chromosome 17p, partial deletion [del(17p)], t(4;14), t(14;16), t(14;20)

               -  Plasma cell leukemia

               -  PFS of less than 2 years after autologous stem cell transplant

          2. Evidence of engraftment of neutrophils (absolute neutrophil count [ANC] >1000
             cells/mm3) and platelets (platelets >60,000 cells/mm3) [dose escalation phase] and
             >50,000 cells/mm3 [dose expansion phase]).

          3. Achievement of at least a PR prior to allogeneic stem cell transplant

          4. Adequate liver and kidney function

          5. Ability to swallow oral medication

          6. Absence of gastrointestinal symptoms that precludes oral intake and absorption of
             MLN9708

          7. Off antibiotics and amphotericin B formulations, voriconazole or other anti-fungal
             therapy for the treatment of proven, probable or possible infections

          8. ECOG of ≤ 2

          9. Life expectancy ≥3 months

         10. Ability to understand the nature of this study and give written informed consent

        Exclusion Criteria:

          1. Patients with progressive disease when compared to pre-transplant staging as defined
             by IMWG Uniform Response criteria for Multiple Myeloma.

          2. Umbilical cord blood transplant

          3. Patients with > Grade 2 peripheral neuropathy with pain, or ≥ Grade 3 peripheral
             neuropathy per NCI CTCAE Version 4.0

          4. Patients with uncontrolled bacterial, viral, or fungal infections

          5. 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.

          6. Patients who are pregnant or breastfeeding

          7. Most recent chemotherapy ≤21 days and ≤ Grade 1 chemotherapy-related side effects,
             with the exception of alopecia

          8. Use of a study drug ≤21 days or 5 half-lives (whichever is shorter) prior to the first
             dose of MLN9708. For study drugs for which 5 half-lives is ≤21 days, a minimum of 10
             days between termination of the study drug and administration of MLN9708 is required.

          9. Wide field radiotherapy (including therapeutic radioisotopes such as strontium 89)
             administered ≤14 days or limited field radiation for palliation ≤7 days prior to
             starting study drug or has not recovered from side effects of such therapy

         10. Major surgical procedures ≤14 days of beginning study drug, or minor surgical
             procedures ≤7 days. No waiting is required following port-a-cath placement.

         11. Ongoing or active systemic infection. Known diagnosis of human immunodeficiency virus,
             hepatitis B, or hepatitis C

         12. Central Nervous System involvement

         13. Known allergy to any of the study medications, their analogues, or excipients in the
             various formulations of any agent.

         14. Systemic treatment with moderate and strong inhibitors of cytochrome P450 (CYP) 1A2,
             CYP3A, or clinically significant CYP3A inducers, or use of Ginkgo biloba or St. John's
             wort within 14 days before study drug administration in the study.

         15. Presence of other active cancers, or history of treatment for invasive cancer ≤5
             years. Patients with Stage I cancer who have received definitive local treatment and
             are considered unlikely to recur are eligible. All patients with previously treated in
             situ carcinoma (i.e., non-invasive) are eligible, as are patients with history of
             non-melanoma skin cancer.

         16. Graft versus host disease > Grade 2; or GVHD grade 1 or Grade 2 which requires > 0.5
             mg/kg methylprednisolone, or equivalent.

        There are additional Inclusion/Exclusion criteria. The Study Center will determine if you
        meet all criteria and will answer any questions you may have about the trial.