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 normal * Creatinine =\< 1.5 x institutional upper limit of normal OR creatinine clearance \>= 60 mL/min for patients with creatinine levels above institutional normal * Fasting serum glucose =\< 130 mg/dL * Fasting triglycerides =\< 300 mg/dL * Glycosylated hemoglobin (HbA1c) \< 7.0% * Patients must have evaluable or measurable disease by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 * Women of child-bearing potential MUST have a negative serum or urine pregnancy test within 7 days unless prior hysterectomy or menopause (defined as 12 consecutive months without menstrual activity); patients should not become pregnant or breastfeed while on this study; women of child-bearing potential must agree to use 1 highly effective method of contraception and 1 additional effective (barrier) method, at the same time, from the time of signing the informed consent through 90 days (or longer, as mandated by local labeling \[e.g.; United Surgical Partners International (USPI), Summary of Product Characteristics (SmPC), etc;\]) after the last dose of study drug; or agree to practice true abstinence; should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately; male patients, even if surgically sterilized (i.e., status post-vasectomy), who: * Agree to practice highly effective barrier contraception during the entire study treatment period and through 120 days after the last dose of study drug, or * Agree to completely abstain from heterosexual intercourse * Ability to understand and the willingness to sign a written informed consent document * Ability to swallow oral medications Exclusion Criteria: * Patients who have had chemotherapy or radiotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered to =\< grade 1 adverse events due to agents administered more than 4 weeks earlier * Patients who are receiving any other investigational agents * Patients with known brain metastases should be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events * History of allergic reactions attributed to compounds of similar chemical or biologic composition to MLN0128 (TAK-228) or ziv-aflibercept * Uncontrolled intercurrent illness including active infection * Pregnant women are excluded from this study because MLN0128 (TAK-228) and ziv-aflibercept are agents with the potential for teratogenic or abortifacient effects; because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with MLN0128 (TAK-228) and ziv-aflibercept, breastfeeding should be discontinued if the mother is treated with MLN0128 (TAK-228) and ziv-aflibercept; these potential risks may also apply to other agents used in this study * Patients with known human immunodeficiency virus infection are not to be enrolled in the study * History of abdominal fistula, gastrointestinal perforation or intra-abdominal abscess within 28 days or manifestations of malabsorption due to prior gastrointestinal (GI) surgery or GI disease that may alter the absorption of MLN0128 (TAK-228) * New York Heart Association class III or greater congestive heart failure within last 6 months or uncontrolled hyperlipidemia (cholesterol \> 300 mg/dl; triglyceride 2.5 X upper limit of normal \[ULN\] despite lipid lowering agent) within last 3 months * Uncontrolled diabetes (fasting serum glucose \> 130 mg/dl) despite best medical management or poorly controlled diabetes mellitus defined as hemoglobin (Hb)A1c \> 7%; subjects with a history of transient glucose intolerance due to corticosteroid administration are allowed in this study if all other inclusion/exclusion criteria are met * History of uncontrolled hypertension, defined as blood pressure \> 150/95 mmHg, or systolic blood pressure \> 180 mmHg when diastolic blood pressure \< 90 mmHg, on at least 2 repeated determinations on separate days within 3 months prior to study enrollment * Urine protein should be screened by dipstick or urine analysis; for proteinuria \> 1+ or urine protein: creatinine ratio \> 1.0, 24-hour urine protein should be obtained and the level should be \< 2000 mg for patient enrollment * Patients on anticoagulant therapy with unstable dose of warfarin and/or having an out-of- therapeutic range international normalized ratio (INR) (\> 3) within the 4 weeks prior to drug administration * Evidence of clinically significant bleeding diathesis or underlying coagulopathy, non-healing wound * History of any of the following within the last 6 months prior to study entry: * Ischemic myocardial event, including angina requiring therapy and artery revascularization procedures * Ischemic cerebrovascular event, including transient ischemic attack (TIA) and artery revascularization procedures * Requirement for inotropic support (excluding digoxin) or serious (uncontrolled) cardiac arrhythmia (including atrial flutter/fibrillation, ventricular fibrillation or ventricular tachycardia) * Placement of a pacemaker for control of rhythm * Pulmonary embolism * Significant active cardiovascular or pulmonary disease at the time of study entry, including: * Uncontrolled high blood pressure (i.e., systolic blood pressure \> 150 mm Hg, diastolic blood pressure \> 95 mm Hg) * Pulmonary hypertension * Uncontrolled asthma or oxygen (O2) saturation \< 90% by pulse oximetry on room air * Significant valvular disease; severe regurgitation or stenosis by imaging independent of symptom control with medical intervention, or history of valve replacement * Medically significant (symptomatic) bradycardia * History of arrhythmia requiring an implantable cardiac defibrillator * Baseline prolongation of the rate-corrected QT interval (QTc) (e.g. repeated demonstration of QTc interval \> 480 milliseconds, or history of congenital long QT syndrome, or torsades de pointes) * Psychiatric illness/social situations that would limit compliance with study requirements * Have initiated treatment with bisphosphonates less than 30 days prior to the first administration of MLN0128 (TAK-228); concurrent bisphosphonate use is only allowed if the bisphosphonate was initiated at least 30 days prior to the first administration of MLN0128 (TAK-228) * Patients who are taking proton pump inhibitor (PPI) within 7 days before receiving the first dose of study drug or who require treatment with PPIs throughout the trial or those who are taking H2 receptor antagonists within 24 hours of the first dose of study drug * Patients with known history of hepatitis B surface antigen-positive, or known history or suspected active hepatitis C infection are not to be enrolled in the study