Selumetinib and Akt Inhibitor MK-2206 in Treating Patients With Refractory or Advanced Gallbladder or Bile Duct Cancer That Cannot Be Removed By Surgery

Inclusion Criteria

• •Patients must have surgically unresectable histologically confirmed biliary tract adenocarcinoma (defined as gallbladder cancer, extrahepatic and intrahepatic cholangiocarcinoma; this definition excludes ampullary cancers and all tumors of mixed histology); cytological confirmation is not allowed on this study, as tissue is needed for correlative science; fresh tissue (mandatory) AND paraffin embedded tissue (positron emission tomography \[PET\]) from tumor blocks (if available) will be required from patients before enrolling on this study
• •Patients will be required to undergo a biopsy prior to enrolling on the study and will be given the option to have another biopsy around 4 weeks from initiation of treatment
• •Patients must have measurable disease by RECIST 1.1 criteria, 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 computed tomography (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
• •All of the following:
• •* Patients must have received only one prior line of systemic therapy for recurrent or advanced disease
• •* Prior adjuvant therapy (chemotherapy +/- radiation) completed within 6 months of diagnosis of recurrence/metastases is equivalent to one line of prior therapy for metastatic disease
• •* For patients who completed adjuvant therapy \> 6 months prior to diagnosis of recurrence/metastases, progression on 1 prior line of systemic therapy for metastatic disease is required
• •* No prior Akt inhibitors or mitogen-activated protein kinase kinase (MEK) inhibitors allowed
• •* For patients who had having prior cryotherapy, radiofrequency ablation, ethanol injection, transarterial chemoembolization (TACE) or photodynamic therapy, the following criteria must be met
• •* 6 weeks must have elapsed since that therapy
• •* Indicator lesion(s) is/are outside the area of prior treatment or, if the only indicator lesion is inside the prior treatment area, there must be clear evidence of disease progression associated with that lesion
• •* Edges of the indicator lesion are clearly distinct on CT scanning
• •* Prior radiation therapy with or without the use of a fluoropyrimidine as a radiosensitizer in the adjuvant setting will be allowed on study if \> 12 weeks have elapsed since therapy
• •* Prior palliative radiation therapy will be allowed as long as \> 2 weeks have elapsed since therapy
• •Life expectancy of greater than 12 weeks
• •Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%)
• •Leukocytes\>= 3,000/µL
• •Absolute neutrophil count \>= 1,500/µL
• •Platelets \>= 100,000/µL
• •Total bilirubin =\< 1.5 X institutional upper limit of normal
• •Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 X institutional upper limit of normal OR =\< 5 X institutional upper limit of normal for intrahepatic cholangiocarcinoma if thought to be related to disease
• •Creatinine within normal institutional limits OR creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal
• •The effects of MK-2206 and AZD6244 hydrogen sulfate on the developing human fetus at the recommended therapeutic dose are unknown; for this reason and because AZD6244 hydrogen sulfate and MK-2206 is known to be teratogenic, women of childbearing potential and men must use two forms of contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation; should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, the patient should inform the treating physician immediately
• •Ability to understand and the willingness to sign a written informed consent document
• •Ability to swallow oral tablets and capsules