Testing MLN0128 (TAK-228) as Potentially Targeted Treatment in Cancers With mTOR Genetic Changes (MATCH - Subprotocol L)

Inclusion Criteria: * Patients must have met applicable eligibility criteria in the Master MATCH Protocol EAY131/ NCI-2015-00054 prior to registration to treatment subprotocol * Patients must fulfill all eligibility criteria of MATCH Master Protocol at the time of registration to treatment step (Step 1, 3, 5, 7) * Patients must have a mutation in mTOR, KEAP1 or NFE2L2 as determined via the MATCH Master Protocol * Patients must have an electrocardiogram (ECG) within 8 weeks prior to treatment assignment and must NOT have any of the following cardiac criteria: * Clinically important abnormalities in rhythm, conduction or morphology of resting ECG (e.g. complete left bundle branch block, third degree heart block, Corrected QT Interval \[QTc\] interval \> 480 milliseconds) * Uncontrolled hypertension (i.e., systolic blood pressure \>180 mm Hg, diastolic blood pressure \> 95 mm Hg). Use of anti-hypertensive agents to control hypertension before cycle 1, day 1 is allowed * Known pulmonary hypertension. * Patients must not have known hypersensitivity to MLN0128 or compounds of similar chemical or biologic composition * Patients must not have known hepatitis B surface antigen-positive, or known or suspected active hepatitis C infection, but may have had previously treated and successfully eradicated hepatitis C virus (HCV) * Patients must have none of the following within six months of receiving the first dose of MLN0128 (TAK-228): ischemic, myocardial or cerebrovascular even…