This study is open to adults with advanced cancer (solid tumors) and people with advanced head and neck cancer. The study has 2 parts. The purpose of Part 1 of this study is to find the highest dose of a medicine called BI 765179 that people with solid tumors can tolerate when taken alone or together with a medicine called ezabenlimab. The goal of Part 2 is to find out whether BI 765179 in combination with a medicine called pembrolizumab helps people with advanced head and neck cancer. In Part 1, each participant is put into 1 of 2 groups. Participants get BI 765179 alone or in combination with ezabenlimab as infusion into a vein every 3 weeks. In Part 2, participants are also divided into 2 groups. 1 group gets a low dose of BI 765179 in combination with pembrolizumab and the other group gets a high dose of BI 765179 in combination with pembrolizumab. Participants receive the study treatment as infusions into a vein. BI 765179, ezabenlimab, and pembrolizumab are antibodies that may help the immune system fight cancer. In this study, BI 765179 is given to people for the first time. Participants can stay in the study up to 2 years if they benefit from treatment and can tolerate it. The doctors regularly check the participants' health and note any health problems that could have been caused by the study treatment.
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Phase 1a: Maximum Tolerated Dose (MTD)
Timeframe: Up to Day 21 (end of Cycle 1)
Phase 1a: Occurrence of Dose Limiting Toxicities (DLTs) in the MTD evaluation period
Timeframe: Up to Day 21 (end of Cycle 1)
Phase 1b: Objective response (OR)
Timeframe: Up to 2 years.