Sirolimus, Gemcitabine Hydrochloride, and Cisplatin in Treating Patients At High Risk for Cholangiocarcinoma Recurrence After Liver Transplant or Surgery

Inclusion Criteria: * Histologic proof of presence of residual tumor in liver explants and /or positive resection margins * Absolute neutrophil count (ANC) \>= 1500/μL obtained =\< 7 days prior to registration * Platelets (PLT) \>= 100,000/μL obtained =\< 7 days prior to registration * Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN) obtained =\< 7 days prior to registration * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 2.5 x ULN obtained =\< 7 days prior to registration (=\< 5 x ULN in patients with liver metastases) * Creatinine =\< 1.5 x Institutional ULN obtained =\< 7 days prior to registration * Alkaline phosphatase =\< 5 x institutional ULN obtained =\< 7 days prior to registration * Hemoglobin (Hgb) \>= 9.0 g/dL obtained =\< 7 days prior to registration * International normalized ratio (INR) and partial thromboplastin (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 obtained =\< 7 days prior to registration * Fasting serum cholesterol =\< 300 mg/dL OR =\< 7.75 mmol/L AND fasting triglycerides =\< 2.5 x ULN obtained =\< 90 days prior to registration; 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 months * Women of childbearing potential only: negative serum pregnancy test done =\< 7 days prior to registration * Four months post liver transplant Exclusion Criteria: * 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 * Taking strong inhibitors or strong/moderate inducers of cytochrome P450 (CYP)3A4 * Strong inhibitors of CYP3A4/5; \> 5-fold increase in the plasma area under the curve (AUC) values or more than 80% decrease in clearance * Clarithromycin (Biaxin®, Biaxin XL®) * Conivaptan (Vaprisol®) * Grapefruit juice * Itraconazole (Sporanox®) * Ketoconazole (Nizoral®) * Mibefradil * Nefazodone (Serzone®) * Posaconazole (Noxafil®) * Telaprevir (Incivek®) * Telithromycin (Ketek®) * Use of the following inducers are prohibited =\< 7 days prior to registration * Strong inducers of CYP3A4/5; \> 80% decrease in AUC * Avasimibe * Carbamazepine (Carbatrol®, Epitol®, Equetro™, Tegretol®, Tegretol-XR®) * Phenytoin (Dilantin®, Phenytek®) * Rifampin (Rifadin®) * St. John's wort * Moderate inducers of CYP3A4/5; 50-80% decrease in AUC * Bosentan (Tracleer®) * Modafinil (Provigil®) * Nafcillin * Phenobarbital (Luminal®) * Rifabutin (Mycobutin®) * Troglitazone * 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 * Biologic 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 surgery or chemotherapy regardless of interval since last treatment * Any of the following because this study involves cytotoxic agents * 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 with low cluster of differentiation (CD)4 count; Note: previous calcineurin inhibitor or previous sirolimus use allowed * Current active other malignancy, except non-melanoma skin cancer or carcinoma-in-situ of the cervix; if there is a history of prior malignancy, they must not be receiving other specific treatment (other than hormonal therapy) for their cancer * Current impairment of gastrointestinal function or gastrointestinal disease that may significantly alter the absorption of sirolimus (e.g., active ulcerative disease, uncontrolled nausea, vomiting, diarrhea, malabsorption syndrome or small bowel resection) * Current severely impaired lung function (i.e., forced expiratory volume in 1 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 sirolimus; examples of live vaccines include intranasal influenza, measles, mumps, rubella, oral polio, Bacillus Calmette-Guérin (BCG), yellow fever, varicella and typhoid (TY)21a typhoid vaccines * Current severe hepatic impairment; 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