Study of Safety and Tolerability of Nivolumab Treatment Alone or in Combination With Relatlimab or Ipilimumab in Head and Neck Cancer

This study is testing nivolumab (an immunotherapy drug) alone or combined with either relatlimab or ipilimumab in people with newly diagnosed, locally advanced head and neck cancer (squamous cell carcinoma) that has not yet been treated with chemotherapy or radiation. The goal is to find better first-line treatment options. **You may be eligible if...** - You are 18 years or older - You have been newly diagnosed with Stage III or IVA squamous cell carcinoma of the head and neck - You have not received radiation or chemotherapy for this cancer (though a surgically removed earlier cancer more than 5 years ago may be acceptable) - Your tumor is accessible for a biopsy before treatment - If your cancer is HPV-positive oropharyngeal cancer: specific tumor and lymph node size criteria must be met **You may NOT be eligible if...** - You have already received systemic treatment (chemotherapy, radiation, or immunotherapy) for your current cancer - Cancer has spread to distant organs - You have conditions that make immunotherapy unsafe - A baseline biopsy cannot be obtained Talk to your doctor to see if this trial is right for you.