A Study to Test Different Doses of BI 765049 Alone and in Combination With Ezabenlimab in Asian People With Advanced Cancer (Solid Tumours) Positive for B7-H6

Inclusion Criteria: Signed and dated, written inform consent form (ICF) (ICF1 for B7-H6 testing for all patients except those with colorectal cancer (CRC); ICF2 for all patients) describing the study in accordance with International Council on Harmonisation Good Clinical Practice (ICH-GCP) and local legislation prior to any trial-specific procedures, sampling, or analyses. ≥18 years of age at the time of signature on the ICFs (ICF1 and ICF2). Histologically or cytologically confirmed diagnosis of an advanced, unresectable, and/or metastatic gastrointestinal cancer, colorectal cancer, pancreatic cancer, liver cancer, head and neck cancer, or lung cancer. Disease progression despite conventional treatment, intolerant to or not a candidate for conventional treatment, or with a tumour for which no conventional treatment exists. Agree to the collection of tumour samples (as slides from archival diagnostic samples or fresh tumour biopsies) for confirmation of B7-H6 expression at Screening Visit 02 for colorectal cancer (CRC) patients or at Screening Visit 01 for all other patients. Confirmed B7-H6 expression on tumour tissue sample (archived or fresh tumour biopsy) based on central pathology review except for patients diagnosed with advanced or metastatic colorectal cancer (CRC). Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1. At least one evaluable target lesion as defined per response evaluation criteria in solid tumors (RECIST v1.1), outside of the central nervous system (CNS), separate from any lesion(s) identified for tumour biopsy. Tumour lesions that have been irradiated ≥28 days before the start of treatment, and have subsequently had documented progression, may be chosen as target lesions only in the absence of measurable lesions that have not been irradiated. Further inclusion criteria apply Exclusion Criteria: History of a major surgery within 28 days prior to first dose of BI 765049 (major according to the Investigator's assessment). Presence of other active invasive cancers other than the one treated in this trial within 3 years prior to screening, except for appropriately treated basal cell carcinoma of the skin, in situ carcinoma of the uterine cervix, or other local tumours considered cured by local treatment. Known leptomeningeal disease or spinal cord compression due to disease. Require anticoagulant treatment which cannot be safely interrupted, if medically needed for a study procedure (e.g., biopsy) based on the opinion of the Investigator. Any of the following laboratory evidence of hepatitis virus infection. Test results obtained in routine diagnostics are acceptable for screening if done within 14 days before the ICF2 date: positive results of hepatitis B surface (HBs) antigen, presence of hepatitis B core (HBc) antibody together with hepatitis B virus (HBV)-DNA and presence of hepatitis C-RNA Infection requiring systemic antimicrobial, antiviral, antiparasitic, or antifungal therapy at the start of treatment in the trial unless otherwise stipulated. Patients with history of human immunodeficiency virus (HIV) infection who meet one or more of the following criteria: cluster of differentiation 4 (CD4)+ count <350 cells/μL, viral load >400 copies/μL, not receiving antiretroviral therapy, receiving established antiretroviral therapy for less than four weeks prior to the start of study treatment, and history of AIDS-defining opportunistic infections within 12 months prior to start of study treatment. Patients with a history of HIV who do not meet any of the criteria above are eligible to participate, but the patient must be under the care of a HIV/Infectious Diseases specialist, or a HIV/Infectious Diseases specialist must be consulted prior to inclusion. Previous treatment history: previous treatment in this trial or another trial with a B7-H6 targeting agent, treatment with a systemic anti-cancer therapy or investigational drug within 21 days or 5 half-lives (whichever is shorter) of the first administration of BI 765049, and treatment with extensive field radiotherapy including whole brain irradiation within14 days prior to first administration of BI 765049. Further exclusion criteria apply