PI3Kbeta Inhibitor AZD8186 and Docetaxel in Treating Patients Advanced Solid Tumors With PTEN or PIK3CB Mutations That Are Metastatic or Cannot Be Removed by Surgery

Inclusion Criteria: * 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 must be able to swallow and retain oral medications and be without gastrointestinal illnesses that would preclude absorption of AZD8186 * Unlimited prior therapies allowed * Docetaxel appropriate * Patients who have not received prior docetaxel (or other taxane therapy) in the advanced setting are eligible for all cohorts * Patients who have previously received docetaxel (or other taxane therapy) in the advanced setting are eligible for the dose escalation cohort only, if anticipated to have maintained taxane sensitivity and in the opinion of the investigator would still benefit from further docetaxel therapy * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%) * Leukocytes \>= 3,000/mcL * Absolute neutrophil count \>= 1,500/mcL * Hemoglobin \>= 8 g/L * Platelets \>= 100,000/mcL * Total bilirubin within normal institutional limits * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 1.5 x institutional upper limit of normal * Creatinine within normal institutional limits OR creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal * PTEN or PIK3CB mutated a…