Mitotane With or Without Cisplatin and Etoposide After Surgery in Treating Patients With Stage I-III Adrenocortical Cancer With High Risk of Recurrence

Inclusion Criteria: * Have a histologically confirmed diagnosis of ACC (Weiss score of \>= 3). (LinWeiss-Bisceglia system will be used for oncocytic ACC). * Have a high risk of relapse defined as: Stage I-III ACC (according to the European Network for the Study of Adrenal Tumors \[ENSAT\] classification) within 90 days of surgical resection of primary tumor with curative intent with either microscopically complete resection (R0, defined as no evidence of microscopic residual disease according to surgical reports, histopathology, and perioperative imaging), microscopically positive margins (R1), or undetermined margins (RX, based on surgical or pathological reports without unequivocal evidence of metastasis in the perioperative imaging). Each participating center will determine the pathological stages and resection margins AND Ki67 \> 10% (to be determined by an experienced pathologist in each participating center and preferably via quantitative imaging analysis). * Have perioperative imaging (computed tomography \[CT\] with contrast, magnetic resonance imaging \[MRI\] of the chest/abdomen/pelvis, or fluorodeoxyglucose positron emission tomography \[FDG-PET\] CT) without unequivocal evidence of disease within 8 weeks before randomization. Patients with indeterminate non-specific nodules (\< 1 cm for soft tissue lesions and \< 1.5 cm in the short dimension for lymph nodes) will be permitted to participate in this study. * Have an Eastern Cooperative Oncology Group (ECOG) performance status 0-2. * Be able to comply with the protocol procedures. * Provide written informed consent. Exclusion Criteria: * The time between primary surgery and randomization \> 90 days. * Gross residual disease after surgery (R2 resection) * High suspicion for metastatic disease on perioperative imaging * They have undergone repeated surgery for recurrence of disease. * They have a history of recent or active prior malignancy, except for cured non-melanoma skin cancer, cured in situ cervical carcinoma, breast ductal carcinoma in situ, or other treated malignancies where there has been no evidence of disease for at least 2 years. * They have renal insufficiency (estimated glomerular filtration rate \[GFR\] \< 50 mL/min/1.73 m\^2). * They have significant liver insufficiency (serum bilirubin \> 2 times the upper normal range) * They have significant liver insufficiency (serum alanine aminotransferase \[ALT\] or aspartate aminotransferase \[AST\] \> 3 times the upper normal range) * Impaired bone marrow reserve (neutrophils \< 1000/mm\^3) * Impaired bone marrow reserve (platelets \< 100,000/mm\^3) * Pregnancy or breast feeding. * They have known congestive heart failure (ejection fraction \< 45%). The extent of cardiac testing will depend on the judgment of the local principal investigator (PI). In general, in patients with a history of cardiac disease, it is recommended to obtain a baseline two-dimensional echocardiogram as standard of care to document ejection fraction. In patients without prior cardiac disease, a baseline electrocardiogram (EKG) is sufficient if there is no evidence of acute ischemic changes or prior evidence of myocardial infarction. If EKG results are abnormal (ischemic changes, significant arrhythmia, or suggestion of prior myocardial infarction), a two-dimensional echocardiogram will be obtained to assess ejection fraction. Cardiac imaging and EKG may not be needed in patients assigned to mitotane who do not have prior cardiac history and have low suspicion for cardiac symptoms to reflect standards of clinical practice. Similarly, utilizing cardiac imaging and EKG within the past 12 months is permitted if there is no suspicion for cardiac issues. * They have preexisting grade 2 peripheral neuropathy. * They underwent previous or current treatment with mitotane or other antineoplastic drugs for ACC. * They underwent previous radiotherapy for ACC. * They have any other severe acute or chronic medical or psychiatric condition or laboratory abnormality that would, in the judgment of the investigator, pose excess risk associated with study participation or administration of the involved drugs or that, in the judgment of the investigator, would make the patient inappropriate for entry into this study.