Sapanisertib and Ziv-Aflibercept in Treating Patients With Recurrent Solid Tumors That Are Metastatic or Cannot Be Removed by Surgery

Inclusion Criteria: * Patients with advanced or metastatic cancer that is refractory to standard therapy or relapsed after standard therapy; patients must have histologically confirmed malignancy that is metastatic or unresectable and for which standard curative or palliative measures do not exist or are no longer effective * Patients enrolled in the expansion cohort must have biopsiable disease; there will be preferential enrollment of patients with pancreatic neuroendocrine tumors or ovarian cancer during the dose expansion cohort * Patients must be \>= 4 weeks beyond treatment of any chemotherapy, other investigational therapy, hormonal, biological, targeted agents or radiotherapy, and must have recovered to =\< grade 1 toxicity or previous baseline for each toxicity; exception: patients may have received palliative low dose radiotherapy to the limbs 1-4 weeks before this therapy provided pelvis, sternum, scapulae, vertebrae, or skull were not included in the radiotherapy field * Eastern Cooperative Oncology Group (ECOG) performance status =\< 1 * Life expectancy of greater than 3 months * Leukocytes \>= 3,000/mcL * Absolute neutrophil count \>= 1,500/mcL * Platelets \>= 100,000/mcL * Hemoglobin \>= 9 g/dL * Total bilirubin =\< 1.5 x institutional upper limit of normal * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x institutional upper limit of n…