This phase III trial studies how well mitotane alone works compared to mitotane with cisplatin and etoposide when given after surgery in treating patients with adrenocortical cancer that has a high risk of coming back (recurrence). Cortisol can cause the growth of adrenocortical tumor cells. Antihormone therapy, such as mitotane, may lessen the amount of cortisol made by the body. Drugs used in chemotherapy, such as cisplatin and etoposide, 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. It is not yet known whether mitotane alone or mitotane with cisplatin and etoposide after surgery works better in treating patients with adrenocortical carcinoma.