Everolimus in Treating Patients With Previously Treated Unresectable or Metastatic Esophageal Cancer or Stomach Cancer

Inclusion criteria: * Diagnosis of adenocarcinoma of the upper gastrointestinal tract * Metastatic or unresectable disease * Received 1-2 prior chemotherapy or biological therapy regimens for unresectable or metastatic disease * Measurable disease in ≥ 1 dimension by CT scan or MRI * Patients whose only measurable lesion is a metastatic lymph node are eligible provided they have permission from the principal investigator * ECOG performance status 0-1 * Life expectancy \> 3 months * ANC ≥ 1,500/mm\^3 * Platelet count ≥ 100,000/mm\^3 * Hemoglobin ≥ 9 g/dL * Total bilirubin ≤ 1.5 times upper limit of normal (ULN) * AST and ALT ≤ 2.5 times ULN (≤ 5.0 times ULN if there is liver metastasis) * Creatinine clearance \> 60 mL/min * Fasting serum cholesterol \< 300 mg/dL or \< 7.75 mmol/L\* * Fasting triglycerides \< 2.5 times ULN\* * INR ≤ 3.5 (for patients on warfarin) * Negative pregnancy test * Fertile patients must use effective contraception during and for ≥ 4 months after completion of study treatment (oral, implantable, or injectable contraceptives are not considered effective contraception for this study) * More than 30 days since prior chemotherapy, surgery, radiotherapy, or investigational agents Exclusion Criteria: * uncontrolled diabetes mellitus, defined as fasting serum glucose \> 1.5 times ULN * severely impaired lung function * known HV infection * active, bleeding diathesis * unstable angina pectoris, symptomatic congestive heart failure, or myocardial infarction within the past 6 months * serious uncontrolled cardiac arrhythmia * active or uncontrolled infection requiring parenteral antimicrobials * known liver disease (e.g., cirrhosis, chronic active hepatitis, or chronic persistent hepatitis) * inability to swallow, impaired gastrointestinal (GI) function, or GI disease (e.g., ulcerative colitis, uncontrolled nausea, vomiting, diarrhea, malabsorption syndrome, or small bowel resection) that would significantly alter the absorption of study drugs or preclude the use of oral medications * other malignancy within the past 5 years except for nonmelanoma skin cancer or cervical carcinoma in situ * known hypersensitivity to everolimus, sirolimus, or temsirolimus or to their excipients * other medical conditions that, in the opinion of the investigator, would preclude study participation * prior mTOR inhibitors (e.g., rapamycin, CCI-779) * concurrent chronic treatment with steroids or another immunosuppressive agent * concurrent prophylactic use of hematopoietic growth factors * concurrent anticancer agents or therapy (including radiotherapy) * other concurrent experimental agents * concurrent strong inhibitors or inducers of the isoenzyme CYP3A4