This pilot phase I trial studies the side effects and best way to give sirolimus, gemcitabine hydrochloride, and cisplatin in treating patients at high risk for cholangiocarcinoma recurrence after liver transplant or surgery. Sirolimus may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Drugs used in chemotherapy, such as gemcitabine hydrochloride, and cisplatin, work in different ways to stop the growth of tumor cells, either by killing the cells or by stopping them from dividing. Giving sirolimus with gemcitabine hydrochloride and cisplatin may prevent disease recurrence in patients with a high risk of recurrence after a liver transplant or surgery.