Brief Summary: This phase I trial studies the side effects and best dose of raptor/rictor-mammalian target of rapamycin (mTOR) (TORC1/2) inhibitor MLN0128 when given in combination with bevacizumab in treating patients with glioblastoma, a type of brain tumor, or a solid tumor that has spread and not responded to standard treatment. TORC1/2 inhibitor MLN0128 may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Monoclonal antibodies, such as bevacizumab, may interfere with the ability of tumor cells to grow and spread. Bevacizumab may also stop the progression of tumors by blocking the growth of new blood vessels necessary for tumor growth.

Detailed Description: PRIMARY OBJECTIVES: I. To determine the maximum tolerated dose and recommended phase 2 dose (MTD/RP2D) of daily oral MLN0128 (TORC1/2 inhibitor INK128) when administered with bevacizumab in patients with advanced solid tumors including recurrent glioblastoma (GBM). II. To evaluate the overall safety and tolerability of the combination of MLN0128 and bevacizumab. SECONDARY OBJECTIVES: I. To assess the preliminary anti-tumor activity of the combination of MLN0128 and bevacizumab, as determined by response rate (RR), progression-free survival (PFS) and overall survival (OS). II. To assess tolerability throughout study therapy with MLN0128 and bevacizumab, including beyond the MTD interval with the following measures of cumulative treatment-related toxicities: frequency of toxicities leading to missed doses or delays; percentage of cycles given or not within 7 days of their scheduled times; percentage of actual planned dosage administration; percentage of patients that discontinue study drugs due to treatment related toxicity. TERTIARY OBJECTIVES: I. To assess cerebrospinal fluid (CSF) penetration of MLN0128 in combination with bevacizumab in patients with recurrent GBM by evaluating the plasma and CSF concentrations of MLN0128 in the absence and presence of bevacizumab. II. To perform archival tumor analysis for markers of dysregulated cell signaling that may predict response to mechanistic target of rapamycin (mTOR) inhibitor therapy such as epidermal growth factor receptor (EGFR) (expression by immunohistochemistry \[IHC\] and amplification by fluorescent in situ hybridization \[FISH\]), phosphatase and tensin homolog (PTEN) (expression by IHC and deletion by FISH), phosphorylated (p)-protein kinase B (AKT), p-ribosomal protein S6 kinase (S6K), p-eukaryotic translation initiation factor 4E binding protein 1 (4EBP), p-mTOR and p-mitogen-activated protein kinase 1 (Erk) in patients with recurrent GBM. III. To analyze select phosphorylated proteins (ERK, AKT, mTOR, 4EBP1, glycogen synthase kinase 3-beta \[GSK3beta\], ribosomal protein S6 kinase, 70kDa, polypeptide 2 \[p70S6K\], rS6) from tumor biopsies obtained at baseline and after treatment with MLN0128 from endometrial and ovarian cancer patients enrolled in stage 2. IV. To analyze circulating plasma levels of angiogenic growth factors before, during and after treatment with MLN0128 and bevacizumab V. To perform genetic mutation analysis and proteomic analysis of tissue from biopsies of endometrial and ovarian cancer patients including analysis of Kirsten rat sarcoma viral oncogene homolog (KRAS), v-raf murine sarcoma viral oncogene homolog B (BRAF), phosphatidylinositol-4,5-bisphosphate 3-kinase, catalytic subunit alpha (PIK3CA), v-akt murine thymoma viral oncogene homolog 1 (AKT1) and PTEN. OUTLINE: This is a dose-escalation study of MLN0128. Patients receive TORC1/2 inhibitor MLN0128 orally (PO) once daily (QD) and bevacizumab intravenously (IV) over 30-90 minutes on days 1 and 15. Courses repeat every 28 days in the absence of disease progression or unacceptable toxicity. After completion of study treatment, patients are followed up for 30 days and then annually thereafter.