Alisertib in Treating Patients With Advanced or Metastatic Sarcoma

PRIMARY OBJECTIVES: I. To determine the response rate (complete response \[CR\] + partial response \[PR\]) assessed for patients within each cohort: liposarcoma (cohort 1); leiomyosarcoma (non-uterine) (cohort 2); undifferentiated sarcoma (including pleomorphic undifferentiated sarcoma, formerly known as malignant fibrous histiocytoma, and myxofibrosarcoma) (cohort 3); malignant peripheral nerve sheath tumor (cohort 4); and other sarcomas (cohort 5). SECONDARY OBJECTIVES: I. To estimate the progression-free survival (PFS) and overall survival (OS) for patients treated with MLN8237 (alisertib) in each cohort. II. To assess the adverse events associated with patients treated with MLN8237 in each cohort. TERTIARY OBJECTIVES: I. To correlate potential clinical benefit with markers of aurora kinase inhibition in pre- and post-treatment tumor biopsies. II. To correlate clinical outcome with change in fluorine F 18 fluorothymidine (FLT)-positron emission tomography (PET) uptake at baseline versus after one week of treatment (ie, week 2 of cycle 1). OUTLINE: Patients receive alisertib orally (PO) twice daily (BID) on days 1-7. Courses repeat every 21 days in the absence of disease progression or unacceptable toxicity. After completion of study treatment, patients are followed up every 6 months for 18 months.