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-303 as a monotherapy and in combination with budigalimab, (ABBV-181). ABBV-303 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-303 as a single agent or in combination with budigalimab (another investigational drug) at different doses. Approximately 181 adult participants will be enrolled in the study across sites worldwide. In Part A, ABBV-303 will be intravenously (IV) infused in escalating doses as a monotherapy in participants with relapsed (R)/refractory (R) solid tumors, R/R non-small cell lung cancer (NSCLC), R/R renal cell carcinoma (RCC), R/R head and neck squamous cell carcinoma (HNSCC), or R/R tissue agnostic participants with mesenchymal epithelial transition. In Part B, ABBV-303 in combination with budigalimab will be IV infused in participants with R/R solid tumors or NSCLC. The estimated duration of the study is up to 3 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 medical assessments, blood tests, and scans.