Sapanisertib or Pazopanib Hydrochloride in Treating Patients With Locally Advanced or Metastatic Sarcoma

Inclusion Criteria: * Patients must have slides available for submission to central pathology review; this review is mandatory prior to registration to confirm eligibility and proper cohort assignment * HISTOLOGIC COHORT 1: Undifferentiated pleomorphic sarcoma (includes: malignant fibrous histiocytoma, myxofibrosarcoma, high grade sarcoma not otherwise specified \[NOS\]) * HISTOLOGIC COHORT 2: Leiomyosarcoma (either uterine or extra-uterine) * HISTOLOGIC COHORT 3: Other (either malignant peripheral nerve sheath tumor or synovial sarcoma); during the phase II portion of the study, enrollment will be limited to maximum of 25 patients in this cohort * Note that the phase I is limited to the histologic subtypes listed above; since patients will be enrolling onto dose cohorts during the phase I, they will not enroll onto specific histologic cohorts, although the histologic subtype informed will be collected during patient enrollment * Histologic documentation: Eligible patients must have histopathologically confirmed sarcoma of one of the subtypes listed, by central review * Locally advanced or metastatic disease; locally advanced disease is defined as disease not amenable to local therapy such as surgery and/or radiation * Measurable disease * Progression on at least one prior systemic chemotherapy for advanced, unresectable or metastatic disease; prior adjuvant or neoadjuvant therapy is not included as prior systemic chemotherapy unless treatment occurred within the…