Brentuximab vedotin at a fixed dose of 1.8 mg/kg will be administered on Day 1 every three weeks as a 30-minute outpatient intravenous infusion. MLN8237 will be orally administered in two divided doses from Days 1-7. The starting dose (level 0) of MLN8237 will be 60 mg daily given in two divided doses (30 mg qAM, 30 mg qPM).The dose of MLN8237 will be escalated in 20-mg increments up to 100 mg daily and de-escalated in 20-mg decrements to 40 mg daily. The fixed dose of brentuximab vedotin on Day 1 and daily dose of MLN8237 on Day 1-7 will constitute one treatment cycle. If no DLTs are observed in the last study cohort, the cohort will be expanded to include a total of 12 patients. If a de-escalation dose is required because 2 or more patients experience DLTs, the next lower cohort will be studied. If 2 or more patients do not experience DLTs, this dose will be declared the MTD. This cohort will be expanded to include 12 patients in order to study the biological endpoints and clinical benefit of the combination. If at any point during the expansion cohort phase of the trial 33% or more of the patients treated at the MTD/maximum administered dose experience a DLT, accrual of additional patients at this does level will cease and the next lowest dose may be explored.