This study is designed to learn more about the effects of Petosemtamab, an investigational drug not FDA approved, compared to standard of care treatment for people with head and neck cancer that has been previously treated with immunotherapy and chemotherapy. If decided to take part in this study, participants will go through a screening period, treatment period, and follow-up period. During the screening period following signing of consent form participants will be evaluated for screening criteria and determined if they qualify for the study. During treatment period participants will be randomly assigned to either receiving petosemtamab or one of the three standard of care choices. In the follow up period the side effects after completion of petosemtamab administration or assigned standard of care treatment will be evaluated. Also, approximately every 12 weeks after study treatment stopped, either petosemtamab or assigned standard of care, participants will receive a phone call for long term follow-up for up to 1.5 years. Participation in this study may last up to two years. The participants will complete questionnaires to evaluate the differences in the quality of life for participants that received petosemtamab versus standard of care treatment. Some serious risk related to this study are infusion related reactions, rash and diarrhea. There may not a benefit from joining the study. The head and neck cancer may improve while on this study but it may not, and it may even get worse. It will also help inform how well Petosemtamab works at curing this type of cancer. The study results may be used to help others in the future.

The purpose of this study is to evaluate investigational treatments (study drug) in people with recurrent or metastatic PD-L1-positive, HPV-negative head and neck squamous cell carcinoma without prior treatment. The goal is to determine the optimal dose level, safety, and tolerability for the study drug BCA101. This is a phase 2 study; BCA101 is not FDA approved by the U.S. Food and Drug Administration (FDA). Treatment for this study may be up to 5 years. The procedures include taking study drug intravenously, blood and urine samples, and CT scans. Risks include diarrhea, nausea, vomiting, mouth sore, nose bleed, headache, and skin rash. You 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.