MK2206 in Treating Patients With Advanced Refractory Biliary Cancer That Cannot Be Removed by Surgery

Inclusion Criteria: * Patients must have histologically confirmed biliary tract carcinoma that is surgically unresectable * Cytological confirmation is not allowed on this study, as tissue is needed for correlative science analysis * Either fresh-frozen tissue (FFT) or paraffin-embedded tissue blocks (PETB) will be required from patients before enrolling on this study * No biopsies will be required unless there is insufficient tissue or if the PETB available is more than 12 months old * Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) as ≥ 10 mm with spiral CT scan (CT scan slice thickness no greater than 5 mm) * Malignant lymph nodes will be considered measurable if they are ≥ 15 mm in short axis * Patients must have received one prior therapy for metastatic disease * No prior Akt inhibitors allowed * Patients with known brain metastases should be excluded from this clinical trial * Life expectancy greater than 12 weeks * Eastern Cooperative Oncology Group (ECOG) performance status (PS) =\<2 (Karnofsky \>= 60%) * Leukocytes \>= 3,000/mcL * Absolute neutrophil count (ANC) \>= 1,500/mcL * Platelet count \>= 100,000/mcL * Total bilirubin =\< 1.5 x institutional upper limit of normal (IULN) * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamic pyruvate transaminase \[SGPT\] =\…