Everolimus, Gemcitabine Hydrochloride, and Cisplatin in Treating Patients With Unresectable Solid Tumors Refractory to Standard Therapy

Inclusion Criteria: * Histologic proof of cancer that is now unresectable and refractory to or refused all standard treatment for the disease; exception: cancers in which gemcitabine is considered an appropriate initial treatment option * Cohort III (MTD) Only: Patients with histologic proof of metastatic cholangiocarcinoma or gallbladder carcinoma who have not had previous treatment for metastatic disease or who received gemcitabine \>= 6 months ago as part of adjuvant therapy * Absolute neutrophil count (ANC) \>= 1500/uL * Platelet (PLT) \>= 100,000/uL * Total bilirubin =\< 1.5 x Institutional upper limit of normal (ULN) * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 2.5 x upper limit of normal (ULN) (=\< 5x ULN in patients with liver metastases) * Creatinine =\< 1.5 x Institutional ULN * Alkaline phosphatase =\< 5 x Institutional ULN * Hemoglobin (Hgb) \>= 9.0 g/dL * International normalized ratio (INR) and Partial thromboplastin time (PTT) =\< 3.0 x ULN (anticoagulation is allowed if target INR =\< 3.0 x ULN on a stable dose of warfarin or on a stable dose of low-molecular-weight \[LMW\] heparin for \> 2 weeks at time of registration) * Fasting serum glucose \< 1.5 x ULN * Fasting serum cholesterol =\< 300 mg/dL OR =\< 7.75 mmol/L AND fasting triglycerides =\< 2.5 x ULN; NOTE: In case one or both of these thresholds are exceeded, the patient can only be included after initiation of appropriate lipid lowering medication * Eastern Cooperative Oncology Group (ECOG) Performance Status (PS) 0, 1 or 2 * Ability to provide informed consent * Willingness to return to Mayo Clinic for follow up * Life expectancy \>= 12 weeks * Women of childbearing potential only: Negative serum pregnancy test done =\< 7 days prior to registration Exclusion Criteria: * Known standard therapy for the patient's disease that is potentially curative or definitely capable of extending life expectancy * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Clinically significant cardiac disease, especially history of myocardial infarction =\< 6 months, or congestive heart failure (New York Heart Association \[NYHA\] classification III or IV) requiring use of ongoing maintenance therapy for life-threatening ventricular arrhythmias * Patients taking strong inhibitors or inducers of CYP3A4 * Prior therapy with everolimus * Any of the following prior therapies: * Chemotherapy =\< 4 weeks prior to registration * Mitomycin C/nitrosoureas =\< 6 weeks prior to registration * Immunotherapy =\< 4 weeks prior to registration * Biological therapy =\< 4 weeks prior to registration * Radiation therapy =\< 4 weeks prior to registration * Radiation to \> 25% of bone marrow prior to registration * Failure to fully recover from acute, reversible effects of prior chemotherapy regardless of interval since last treatment * CNS metastases that are not stable for at least 4 weeks prior to registration based on imaging, clinical assessment, and use of steroids * Uncontrolled brain or leptomeningeal metastases, including patients who continue to require glucocorticoids for brain or leptomeningeal metastases * Pregnant women * Nursing women * Men or women of childbearing potential who are unwilling to employ adequate contraception * Other concurrent chemotherapy, immunotherapy, radiotherapy, or any ancillary therapy considered investigational (utilized for a non-Food and Drug Administration \[FDA\]-approved indication and in the context of a research investigation) * Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens * Immunocompromised patients (other than that related to the use of corticosteroids) including patients known to be human immunodeficiency virus (HIV) positive * Current active other malignancy, except non-melanoma skin cancer or carcinoma-in-situ of the cervix * Impairment of gastrointestinal function or gastrointestinal disease that may significantly alter the absorption of everolimus (e.g., ulcerative disease, uncontrolled nausea, vomiting, diarrhea, malabsorption syndrome or small bowel resection) * Severely impaired lung function (i.e., forced expiratory volume in one second \[FEV1\] \< 1 liter) * Received immunization with attenuated live vaccines =\< 7 days prior to study entry or during study period; NOTE: close contact with those who have received attenuated live vaccines should be avoided during treatment with everolimus; examples of live vaccines include intranasal influenza, measles, mumps, rubella, oral polio, BCG, yellow fever, varicella and TY21a typhoid vaccines * Liver disease such as cirrhosis or severe hepatic impairment (Child-Pugh class C); Note: A detailed assessment of Hepatitis B/C medical history and risk factors must be done at screening for all patients; hepatitis B virus (HBV) deoxyribonucleic acid (DNA) and hepatitis C virus (HCV) ribonucleic acid (RNA) polymerase chain reaction (PCR) testing are required at screening for all patients with a positive medical history based on risk factors and/or confirmation of prior HBV/HCV infection