The purpose of this study is to test the effectiveness and safety of the combination of an investigational vaccine, PDS0101, given by subcutaneous (beneath the skin) injection and the standard of care, Pembrolizumab (KEYTRUDA), given intravenously ("IV;" into the vein) compared to pembrolizumab (KEYTRUDA) alone for those with unresectable recurrent or metastatic head and neck cancer and high risk papillomavirus infection. "Investigational" means the combination of the study vaccine and pembrolizumab being tested has not been approved by the US Food and Drug Administration (FDA) nor any other Health Authority.

This study is for subjects who has been diagnosed with radioactive iodine refractory (RAIR) differentiated thyroid cancer. Subjects are expected to remain in the study for a minimum of 96 months. Drugs are FDA approved and is given in the form of Tablet to subjects. The procedures include urine protein test, CT, MRI. Risks include diarrhea, nausea, vomiting, tiredness, weight loss, loss of appetite, changes in taste, redness, pain or peeling of palms and soles, High blood pressure. There is evidence that dabrafenib, trametinib and cabozantinib are effective in stabilizing and shrinking the type of cancer, we do not know which of these approaches are better at prolonging time until tumor growth. However, information learned from the trial may help other people in the future.

This study is for patients diagnosed with unresectable locally recurrent or metastatic head and neck cancer. The purpose of this study is to test if adding an investigational drug called amivantamab to the usual chemotherapy (carboplatin and paclitaxel) is more effective in treating head and neck cancer when compared to being treated with carboplatin and paclitaxel alone. Carboplatin and paclitaxel are FDA approved to treat head and neck cancers; however, adding the study drug, amivantamab, is still being investigated and is not approved by the FDA.

Patients may participate in this study for up to 2 years. Procedures include CT, MRI, blood tests, chemotherapy, and regular visits with your doctor including follow-up study visits or phone calls every 3 months. There will be about 50 people taking part in this study, approximately 3 participants will be enrolled at MUSC.

Risks include constipation, nausea, rash, vomiting, swelling of arms and/or legs. Participants may or may not receive a direct benefit from participating in this trial, however, information learned from the trial may help other people in the future.

This study is for people with advanced head and neck cancer who cannot receive cisplatin. The purpose of this study is to compare treating head and neck cancer with radiation plus cetuximab versus radiation plus chemotherapy (carboplain and paclitaxel). Carboplatin, paclitaxel, and cetuximab are approved by the FDA to treat head and neck cancer.

If you agree to take part, we expect that your participation in this study may last up to 3 years. This includes visits to the clinic after you finish all study treatments. These follow-up visits will take place about every 2 months during the 1st year and about every 4 months thereafter.

Risks may include nausea, vomiting, headache, feeling tired, loss of appetite, and hair loss. Participants may or may not receive a direct benefit from participating in this trial, however, information learned from the trial may help other people in the future.