A Study to Test Whether Different Combinations of BI 765063, Ezabenlimab, Chemotherapy, Cetuximab, and BI 836880 Help People With Head and Neck Cancer or Liver Cancer

With an amendment of the protocol, this study is only open to adults with head and neck cancer. Previously also adults with liver cancer joined. This is a study for people for whom previous treatment was not successful or no standard treatment exists. The purpose of this study is to find out whether combining different medicines make tumours shrink. The tested medicines in this study are antibodies that act in different ways against cancer. BI 765063 and ezabenlimab may help the immune system fight cancer (checkpoint inhibitors). Cetuximab blocks growth signals and may prevent the tumour from growing. BI 836880 blocks the formation of new blood vessels that the tumour needs to grow. With amendments of the protocol, all participants receive cetuximab in addition to BI 765063 and ezabenlimab. Ezabenlimab treatment and any other assigned treatment are given no longer than 2 years. Previously, BI 765063 and ezabenlimab were also given alone, or in combination with chemotherapy, or with BI 836880. BI 765063, ezabenlimab, and BI 836880 are given as infusions into veins every 3 weeks. Cetuximab is given as an infusion every 1 or 2 weeks. Participants can stay in the study as long as they benefit from treatment and can tolerate it. They regularly visit the study site where doctors check participants' health and take note of any unwanted effects. The doctors also monitor the size of the tumour.