This phase II trial tests how well nivolumab and ipilimumab immunotherapy with or without cabozantinib in treating patients with nasopharyngeal cancer that has come back (after a period of improvement) (recurrent), has spread from where it first started (primary site) to other places in the body (metastatic), or for which no treatment is currently available (incurable). 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. Cabozantinib is in a class of medications called kinase inhibitors. It works by blocking the action of an abnormal protein that signals cancer cells to multiply. This helps slow or stop the spread of cancer cells. Giving immunotherapy with nivolumab and ipilimumab and targeted therapy with cabozantinib may help shrink and stabilize nasopharyngeal cancer.

This phase III trial compares the effect of adding cetuximab to pembrolizumab versus pembrolizumab alone in treating patients with head and neck squamous cell carcinoma (HNSCC) that has come back after a period of improvement (recurrent) and/or that has spread from where it first started (primary site) to other places in the body (metastatic). Cetuximab is in a class of medications called monoclonal antibodies. It binds to a protein called EGFR, which is found on some types of tumor cells. This may help keep tumor cells from growing. Immunotherapy with monoclonal antibodies, such as pembrolizumab, may help the body's immune system attack the tumor, and may interfere with the ability of tumor cells to grow and spread. Giving cetuximab and pembrolizumab together may be more effective at treating patients with recurrent and/or metastatic HNSCC than pembrolizumab alone.

This phase II trial studies how well radiation therapy with or without cisplatin works in treating patients with stage III-IV squamous cell carcinoma of the head and neck who have undergone surgery. Radiation therapy uses high energy x-rays to kill tumor cells and shrink tumors. Drugs used in chemotherapy, such as cisplatin, work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. It is not yet known if radiation therapy is more effective with or without cisplatin in treating patients with squamous cell carcinoma of the head and neck.

This phase II / III trial studies how well chemotherapy and radiation therapy with nivolumab or observation work in treating patients with intermediate risk HPV-positive oropharyngeal cancer that has spread to nearby tissue or lymph nodes. Drugs used in chemotherapy, such as cisplatin, work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Radiation therapy uses high energy rays to kill tumor cells and shrink tumors. Immunotherapy with monoclonal antibodies, such as nivolumab, may help the body's immune system attack the cancer, and may interfere with the ability of tumor cells to grow and spread. It is not yet known whether chemotherapy and radiation therapy with nivolumab or observation works better in treating patients with HPV-positive oropharyngeal cancer.

This phase II trial studies the effect of pembrolizumab in combination with radiation therapy or pembrolizumab alone compared to the usual approach (chemotherapy plus radiation therapy) after surgery in treating patients with head and neck squamous cell carcinoma that has come back (recurrent). Radiation therapy uses high energy radiation or protons to kill tumor cells and shrink tumors. Chemotherapy drugs, such as cisplatin and carboplatin, work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Immunotherapy with monoclonal antibodies, such as pembrolizumab, may help the body's immune system attack the cancer, and may interfere with the ability of tumor cells to grow and spread. Giving pembrolizumab in combination with radiation therapy or pembrolizumab alone after surgery may work better than the usual approach in shrinking head and neck squamous cell carcinoma.

This phase III trial compares pembrolizumab with radiation therapy to pembrolizumab without radiation therapy (standard therapy) given after pembrolizumab plus chemotherapy for the treatment of patients with squamous cell carcinoma of the head and neck that has spread from where it first started (primary site) to other places in the body (metastatic). Pembrolizumab is a type of immunotherapy that stimulates the body's immune system to fight cancer cells. Pembrolizumab targets and blocks a protein called PD-1 on the surface of certain immune cells called T-cells. Blocking PD-1 triggers the T-cells to find and kill cancer cells. Radiation therapy uses high-powered rays to kill cancer cells. Giving radiation with pembrolizumab may be more effective at treating patients with metastatic head and neck cancer than the standard therapy of giving pembrolizumab alone.

This phase III trial compares the effect of cabozantinib versus combination dabrafenib and trametinib for the treatment of patients with differentiated thyroid cancer that does not respond to treatment (refractory) and which expresses a BRAF V600E mutation. Cabozantinib is in a class of medications called receptor tyrosine kinase inhibitors. It binds to and blocks the action of several enzymes which are often over-expressed in a variety of tumor cell types. This may help stop or slow the growth of tumor cells and blood vessels the tumor needs to survive. Dabrafenib is an enzyme inhibitor that binds to and inhibits the activity of a protein called B-raf, which may inhibit the proliferation of tumor cells which contain a mutated BRAF gene. Trametinib is also an enzyme inhibitor. It binds to and inhibits the activity of proteins called MEK 1 and 2, which play a key role in activating pathways that regulate cell growth. This may inhibit the growth of tumor cells mediated by these pathways. The usual approach for patients with thyroid cancer is targeted therapy with dabrafenib and trametinib. This trial may help researchers decide which treatment option (cabozantinib alone or dabrafenib in combination with trametinib) is safer and/or more effective in treating patients with refractory BRAF V600E-mutated differentiated thyroid cancer.

This phase II/III trial studies how well sentinel lymph node biopsy works and compares sentinel lymph node biopsy surgery to standard neck dissection as part of the treatment for early-stage oral cavity cancer. Sentinel lymph node biopsy surgery is a procedure that removes a smaller number of lymph nodes from your neck because it uses an imaging agent to see which lymph nodes are most likely to have cancer. Standard neck dissection, such as elective neck dissection, removes many of the lymph nodes in your neck. Using sentinel lymph node biopsy surgery may work better in treating patients with early-stage oral cavity cancer compared to standard elective neck dissection.

This phase II/III trial compares the effect of the combination of high-dose cisplatin every three weeks and radiation therapy versus low-dose cisplatin weekly and radiation therapy for the treatment of patients with locoregionally advanced head and neck cancer. Chemotherapy drugs, such as cisplatin, work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Radiation therapy uses high energy x-rays to kill tumor cells and shrink tumors. This study is being done to find out if low-dose cisplatin given weekly together with radiation therapy is the same or better than high-dose cisplatin given every 3 weeks together with radiation therapy in treating patients with head and neck cancer.

This phase II trial tests whether ado-trastuzumab emtansine works to shrink tumors in patients with HER2-positive salivary gland cancer that has come back (recurrent), spread to other places in the body (metastatic), or cannot be removed by surgery (unresectable). Trastuzumab emtansine is a monoclonal antibody, called trastuzumab, linked to a chemotherapy drug called emtansine. Trastuzumab attaches to HER2 positive cancer cells in a targeted way and delivers emtansine to kill them. Trastuzumab emtansine may work better compared to usual treatment of chemotherapy with docetaxel and trastuzumab in treating patients with salivary gland cancer.

This phase II trial tests the addition of BMS-986016 (relatlimab) to the usual immunotherapy after initial treatment for nasopharyngeal cancer 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). Relatlimab is a monoclonal antibody that may interfere with the ability of tumor cells to grow and spread. The usual approach of treatment is initial treatment with chemotherapy such as the combination of cisplatin (or carboplatin) and gemcitabine, along with immunotherapy such as nivolumab. After the initial treatment is finished, patients may continue to receive additional immunotherapy. Giving BMS-986016 in addition to the usual immunotherapy after initial treatment may extend the time without the tumor cells grow or spread longer than the usual approach in patients with recurrent or metastatic nasopharyngeal cancer.

This randomized phase II/III trial studies how well radiation therapy works when given together with cisplatin compared to docetaxel or cetuximab and docetaxel after surgery in treating patients with stage III-IV squamous cell head and neck cancer. Specialized radiation therapy that delivers a high dose of radiation directly to the tumor may kill more tumor cells and cause less damage to normal tissue. Drugs used in chemotherapy, such as cisplatin and docetaxel, work in different ways to stop the growth of tumor cells, either by killing the cells or by stopping them from dividing. Monoclonal antibodies, such as cetuximab, can block tumor growth in different ways. Some block the ability of tumor cells to grow and spread. Others find tumor cells and help kill them or transmit tumor killing molecules to them. It is not yet known whether radiation therapy is more effective when given with cisplatin, docetaxel, or cetuximab and docetaxel.