Open-label, Phase II Study of MLN9708 in Patients With Relapsed/Refractory Cutaneous and Peripheral T-cell Lymphomas

Inclusion Criteria: * Male or female patients 18 years or older at the time of enrollment. * Voluntary written consent must be given. * Female patients who are postmenopausal for at least 1 year before the screening visit, OR surgically sterile, OR agree to practice 2 effective methods of contraception, at the same time, through 90 days after the last dose of study drug, AND adhere to the guidelines of any treatment-specific pregnancy prevention program, OR agree to practice true abstinence. * Male patients must agree to practice effective barrier contraception through 90 days after the last dose of study drug, OR adhere to the guidelines of any treatment-specific pregnancy prevention program, OR agree to practice true abstinence. * Patients must have histologically proven T-cell lymphoma, including Peripheral T-cell lymphoma, Angioimmunoblastic T-cell lymphoma, Anaplastic large cell lymphoma (ALK positive), Anaplastic large cell lymphoma (ALK negative), Mycosis fungoides, Sezary syndrome. * CTCL patients must have stage IIb-IV disease. * Eastern Cooperative Oncology Group (ECOG) performance status 0, 1, or 2. * Absolute neutrophil count (ANC) ≥ 1,000/mm3 and platelet count ≥ 75,000/mm3. * Platelet transfusions are not allowed within 3 days before study enrollment. * Total bilirubin ≤ 1.5 x the upper limit of the normal range (ULN). * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤ to 3 x ULN. * Creatinine clearance ≥30 mL/min. * Documented disease progression after receiving at least one prior therapeutic regimen. Exclusion Criteria: * Female patients who are lactating or have a positive serum pregnancy test. * Failure to have recovered (ie, less than or equal to Grade 1 toxicity) from the reversible effects of prior chemotherapy. * Major surgery within 14 days of enrollment. * Radiotherapy within 14 days of enrollment. If the field is small, 7 days will be considered a sufficient interval between treatment and administration of the MLN9708. * Known central nervous system involvement. * Infection requiring systemic intravenous antibiotic therapy or other serious infection within 7 days before study enrollment. * Evidence of current uncontrolled cardiovascular conditions, including uncontrolled hypertension, uncontrolled cardiac arrhythmias, symptomatic congestive heart failure, unstable angina, or myocardial infarction within the past 6 months. * Systemic treatment, within 14 days before the first dose of MLN9708, with strong inhibitors of CYP1A2, strong inhibitors of CYP3A or strong CYP3A inducers or use of Ginkgo biloba or St. John's wort. * Ongoing or active systemic infection, active hepatitis B or C virus infection, or HIV positive. * Any serious medical or psychiatric illness that could potentially interfere with the completion of treatment according to this protocol. * Known allergy to any of the study medications, their analogues, or excipients. * 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. * Patient has greater than or equal to Grade 3 peripheral neuropathy, or Grade 2 with pain on clinical examination during the screening period. * Participation in other clinical trials with other investigational agents not included in this trial, within 21days of the start of this trial and throughout the duration of this trial. * Prior allogeneic hematopoietic stem cell transplant. * Prior autologous hematopoietic stem cell transplant within 90 days of study entry. * Prior treatment with bortezomib.