Cancer is a condition where cells in a specific part of body grow and reproduce uncontrollably. The purpose of this study is to assess safety, tolerability, pharmacokinetics and preliminary efficacy of ABBV-711 as a monotherapy and in combination with budigalimab (ABBV-181) in adults with advanced squamous tumors. ABBV-711 is an investigational drug being developed for the treatment of solid tumors. There are multiple treatment arms in this study. Participants will either receive ABBV-711 as a single agent or in combination with budigalimab (another investigational drug) at different doses. Approximately 220 adult participants will be enrolled in the study across 40 sites worldwide. In part 1, oral ABBV-711 tablets will be given in escalating doses alone to participants with squamous (sq) tumors. In part 2 oral ABBV-711 tablets will be given at a selected dose from part 1 to participants with squamous non-small cell lung cancer (sqNSCLC), or head and neck squamous cell carcinoma (HNSCC). In part 3, oral ABBV-711 tablets will be given in escalating doses in combination with intravenously (IV) infused budigalimab to participants with sq tumors. In part 4 oral ABBV-711 tablets will be given at a selected dose from part 3 in combination with IV infused budigalimab to participants with sqNSCLC, or HNSCC. The estimated duration of the study is up to approximately 5 years. There may be higher treatment burden for participants in this trial compared to their standard of care. Participants will attend regular visits during the study at a hospital or clinic and may require frequent questionnaire, medical assessments, blood tests, and scans.