|Exclusion Criteria:||1) Peripheral neuropathy >/= Grade 2 on clinical examination during the Screening period.|
2) Female patients who are lactating or have a positive serum pregnancy test during the Screening period.
3) Major surgery within 14 days before the first dose of study drug.
4) Infection requiring systemic antibiotic therapy or other serious infection within 14 days before the first dose of study treatment.
5) Life-threatening illness unrelated to cancer.
6) Diarrhea > Grade 1, based on the NCI CTCAE categorization.
7) Patient must have recovered from the side effects of previous systemic antineoplastic therapy given within 21 days before the first dose of study treatment.
8) Radiotherapy within 14 days before the first dose of study treatment. If the involved field is small, 7 days will be considered a sufficient interval between treatment and administration of the MLN9708.
9) Treatment with any investigational products within 21 days before the first dose of study treatment.
10) Treatment with any investigational proteasome inhibitor, except carfilzomib. Patients previously treated with carfilzomib may be eligible for the Dose Escalation cohorts if the last dose of carfilzomib was >/= 60 days before the first dose of MLN9708, the Relapsed Refractory MTD expansion cohort if they have refractory disease, or the Carfilzomib cohort regardless of the time since the last dose of carfilzomib.
11) Systemic treatment with strong inhibitors of CYP1A2 (fluvoxamine, enoxacin), strong inhibitors of CYP3A (clarithromycin, telithromycin, itraconazole, voriconazole, ketoconazole, nefazodone) or strong CYP3A inducers (rifampin, rifapentine, rifabutin, carbamazepine, phenytoin, phenobarbital) within 14 days before the first dose of MLN9708.
12) Ongoing therapy with corticosteroids greater than 10 mg of prednisone or its equivalent per day. Inhaled and topical steroids are permitted
13) Central nervous system (CNS) involvement.
14) Evidence of current uncontrolled cardiovascular conditions, including cardiac arrhythmias, congestive heart failure (CHF), angina, or myocardial infarction within the past 6 months.
15) QTc > 470 milliseconds (msec) on a 12-lead ECG obtained during the Screening period. If a machine reading is above this value, the ECG should be reviewed by a qualified reader and confirmed on a subsequent ECG.
16) Known human immunodeficiency virus (HIV) positive.
17) Known hepatitis B surface antigen-positive status, or known or suspected active hepatitis C infection.
18) Any serious medical or psychiatric illness that could, in the investigator's opinion, potentially interfere with the completion of treatment according to this protocol.
19) Known allergy to boron or excipients in the formulation.
20) Known GI disease or GI procedure that could interfere with the oral absorption or tolerance of MLN9708 including difficulty swallowing.