This phase II trial studies the effect of immunotherapy drugs (ipilimumab and nivolumab) in treating patients with glioblastoma that has come back (recurrent) and carries a high number of mutations. Cancer is caused by changes (mutations) to genes that control the way cells function. Tumors with high number of mutations may respond well to immunotherapy. Immunotherapy with monoclonal antibodies such as ipilimumab and nivolumab may help the body's immune system attack the cancer and may interfere with the ability of tumor cells to grow and spread. Giving ipilimumab and nivolumab may lower the chance of recurrent glioblastoma with high number of mutations from growing or spreading compared to usual care (surgery or chemotherapy).