INI1 is a tumor suppressor gene and several aggressive pediatric tumor types are characterized by INI1 negativity, including rhabdoid tumors, epithelioid sarcoma, and chordoma. These cancers represent a portion of rare tumor diagnoses and each are associated with a poor prognosis with few treatment options. Available evidence suggests that there is a low rate of PD-L1 and CTLA-4 expression (proteins that cancer cells use to protect themselves and hide from T-cells) in pediatric cancers and a low rate of response to immune checkpoint inhibitors. However, recently published data suggests that INI1-deficient tumors may be an important exception to this pattern. Thus, this phase II study will evaluate the objective response rate (the percentage of patients whose tumor shrinks or disappears after starting treatment) of nivolumab (PD-1 inhibitor) and ipilimumab (CTLA-4 inhibitor), in pediatric patients with INI1-negative tumors mentioned above. This combination of immune checkpoint inhibitors has been found to be effective in numerous cancer types.