Testing the Addition of an Anti-Cancer Drug, Cabozantinib to the Immunotherapy Drug Cemiplimab (REGN2810), in Adolescents and Adults With Advanced Adrenocortical Cancer

This phase II trial compares the effect of giving cabozantinib with or without cemiplimab in patients with adrenocortical cancer that has spread to nearby tissue or lymph nodes (locally advanced), and that cannot be removed by surgery (unresectable) or that has come back after a period of improvement (recurrent) or that has spread from where it first started (primary site) to other places in the body (metastatic). Cabozantinib is in a class of medications called tyrosine kinase inhibitors. It works by blocking the action of an abnormal protein that signals cancer cells to multiply, which may help keep cancer cells from growing. Immunotherapy with monoclonal antibodies, such as cemiplimab, may help the body's immune system attack the cancer, and may interfere with the ability of tumor cells to grow and spread. Giving cabozantinib with cemiplimab may kill more tumor cells in patients with locally advanced unresectable or recurrent/metastatic adrenocortical cancer.

Inclusion Criteria: * STEP 1: Patients must have documented histologically or cytologically confirmed adrenocortical carcinoma * STEP 1: Locally advanced unresectable or recurrent/metastatic disease * STEP 1: Evaluable disease as defined by RECIST v 1.1 * STEP 1: Up to 3 prior lines of systemic therapy will be allowed in the unresectable/recurrent/metastatic setting. Treatment naïve patients will be allowed. * Note: Combination etoposide, doxorubicin, cisplatin, and mitotane (EDP-M) is considered 1 line of therapy. For patients who received mitotane ≤ 6 months prior to registration, mitotane should be discontinued 28 days prior to study registration AND a mitotane level must be documented to be \< 2 mg/L prior to registration. Patients who have received mitotane within 6 months of enrollment and who have mitotane levels ≥ 2 mg/L will not be eligible to enroll * STEP 1: No prior treatment with cabozantinib or other cMET inhibitors, or anti-CTLA-4, or anti-PD-1/PD-L1 therapy * STEP 1: Prior external beam radiation therapy (any area radiated within a month prior to study registration cannot be used as an index lesion and only growth outside of the radiation field can be considered for disease progression), systemic cytotoxic chemotherapy, targeted therapies will be allowed, as long as not administered within 14 days before study registration, and provided any acute treatment-related associated toxicities have recovered to ≤ grade 1 except for alopecia, peripheral neuropathy or other residual toxicities that are not deemed clinically significant * STEP 1: Potential trial participants should have recovered from clinically significant adverse events, and wound healing is clinically adequate of their most recent therapy/intervention prior to enrollment * STEP 1: Age 12 years and above; and BSA ≥ 1.2m\^2 * STEP 1: * Eastern Cooperative Oncology Group (ECOG) performance 0 - 2 (age 18 and above); or * Patients 12 to \