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 PIK3CA mutations who have access to AND are eligible for Lung-MAP (S1400) are not eligible
* Patients must not have KRAS mutations, and/or PTEN mutation or loss, detected in the tumor sample as determined by the MATCH screening assessment. PTEN loss will be determined by immunohistochemistry
* Patients must not have had prior therapy with a PI3K inhibitor or PI3K/mTOR inhibitor. These include, but are not limited to: BEZ235, XL-765 (SAR245409), GDC-0980, PF-04691502, PF-05212384 (PKI-587), SF-1126, GSK 2126458, P-7170, BGT-226, LY3023414, GDC-0084, DS-7423, BKM-120 (buparlisib), PX-866, XL-147, GDC-0941 (pictilisib), VS-5584, BAY-80-6946, ZSTK-474, WX 037, AZD8835, GSK2636771, GS-9820, BYL719, MLN1117 (INK1117), idelalisib, TGR1202, RP6530, duvelisib (IPI-145), CUDC-907. Prior GDC-0032 (taselisib) is not allowed
* Patients must not have had prior therapy with an Akt inhibitor. These include, but are not limited to: MK-2206, GSK690693, AZD5363, triciribine, perifosine, GSK2141795, GSK2110183, SR13668, BAY1125976, GDC-0068 (ipatasertib), LY2780301, ARQ092
* Patients must not have type 1 or 2 diabetes requiring anti-hyperglycemic medication (e.g. metformin, glipizide, insulin)
* Patients must not have current dyspnea at rest or require any daily supplemental oxygen
* Patients must not have history of inflammatory bowel disease (e.g. Crohn's disease or ulcerative colitis) or active bowel inflammation (e.g. diverticulitis)