This phase I trial studies the side effects and best dose of alisertib when given together with combination chemotherapy in treating patients with gastrointestinal tumors. Alisertib may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Drugs used in chemotherapy, such as fluorouracil, leucovorin calcium, oxaliplatin, work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Giving alisertib with more than one drug (combination chemotherapy) may be a better treatment for gastrointestinal tumors.