This phase I/II trial studies the side effects and how well nivolumab and ipilimumab works when given together with stereotactic body radiation therapy (SBRT) in treating patients with salivary gland cancers. Immunotherapy with monoclonal antibodies, such as nivolumab and ipilimumab, may help the body's immune system attack the cancer, and may interfere with the ability of tumor cells to grow and spread. Stereotactic body radiation therapy uses special equipment to position a patient and deliver radiation to tumors with high precision. This method can kill tumor cells with fewer doses over a shorter period and cause less damage to normal tissue. Giving nivolumab and ipilimumab and SBRT may work better in treating patients with advanced salivary gland cancers.
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Incidence of Toxicity Graded According to the National Cancer Institute Common Terminology Criteria for Adverse Events Version 5.0
Timeframe: From start of treatment through up to 100 days after the completion of study treatment (up to 16 months total)