Testing GDC-0032 (Taselisib) as a Potential Targeted Treatment in Cancers With PIK3CA Genetic Changes (MATCH-Subprotocol I)

Inclusion Criteria: * Patients must have met applicable eligibility criteria in the Master MATCH Protocol prior to registration to treatment subprotocol * Patients must have a PIK3CA mutation as determined via the MATCH Master Protocol * Patients must have an electrocardiogram (ECG) within 8 weeks prior to treatment assignment and must have no clinically important abnormalities in rhythm, conduction or morphology of resting ECG (e.g. complete left bundle branch block, third degree heart block) * Patients with known left ventricular dysfunction must have echocardiogram (ECHO) or multigated acquisition scan (MUGA) within 4 weeks prior to registration to treatment and must not have left ventricular ejection fraction (LVEF) \< institutional lower limit of normal (LLN). If the LLN is not defined at a site, the LVEF must be \> 50% for the patient to be eligible * Patients must have a fasting glucose =\< 125 mg/dL * NOTE: Please provide clear documentation that the glucose test was conducted at a fasting state * Patients with prior treatment with an mTOR inhibitor are acceptable. These include, but are not limited to: temsirolimus, everolimus, ridaforolimus, sirolimus, CC-223, MLN128 (INK128), DS-3078, CC-115, AZD-2014, AZD8055 Exclusion Criteria: * Patients must not have known hypersensitivity to GDC-0032 (taselisib) or compounds of similar chemical or biologic composition * Patients must not have breast cancer * Patients with squamous cell carcinoma of the lung who have PIK3…