A Study Evaluating Different Doses of BI 765049 When Given Alone and When Given With Ezabenlimab to Patients With Advanced Solid Tumors Expressing the Protein B7-H6 on the Cell Surface

Inclusion Criteria: * Signed and dated, written informed consent form (ICF) (ICF1 for B7-H6 testing for all patients except those with advanced or metastatic colorectal cancer (CRC); and 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. * Patient must be ≥18 years of age at the time of signature on the ICFs (ICF1 and ICF2). * Patients with a histologically or cytologically confirmed diagnosis of an advanced, unresectable, and/or metastatic colorectal carcinoma (CRC), non-small cell lung cancer (NSCLC), hepatocellular carcinoma (HCC), head and neck squamous cell carcinoma (HNSCC), gastric carcinoma, and pancreatic carcinoma. At least 1 patient in each back-fill slot must be a non-CRC patient (i.e., NSCLC, HCC, HNSCC, gastric carcinoma, or pancreatic carcinoma). * Patients with disease progression despite conventional treatment, intolerant to or not a candidate for conventional treatment, or with a tumor for which no conventional treatment exists. * All patients must agree to the collection of tumor samples (as slides from archival diagnostic samples or fresh tumor biopsies) for confirmation of B7-H6 expression either at Screening visit 02 (for CRC patients) or Screening visit 01 (for all other patients). To qualify for a back-fill slot or recommended dose expansion (RDE) cohort, the patient must agree to the collection of mandatory pre-treatment and on-treatment fresh tumor biopsies. * Patient diagnosed with advanced or metastatic CRC or patient with confirmed B7-H6 expression on tumor tissue sample (archived or fresh tumor biopsy) based on central pathology review. * Patients with an Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1. * Patient must have at least one evaluable target lesion outside of the central nervous system (CNS) as defined per Response Evaluation Criteria in Solid Tumors (RECIST) v1.1 separate from any lesion(s) identified for tumor biopsy. Tumor lesions that have been irradiated at least ≥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: * Patient with a history of a major surgery within 28 days prior to first dose of BI 765049 (major according to the Investigator's and/or Medical Monitor's assessment). * Patient with a history of a previous or concomitant malignancies. Patient with a malignancy considered effectively treated and cured by 'local treatment' within the last 2 years and that is distinct from the one treated in this trial will be allowed. * Patient with known leptomeningeal disease or spinal cord compression due to disease. * Patient requiring anticoagulant treatment which cannot be safely interrupted, if medically needed for a study procedure (e.g., biopsy) based on the opinion of the Investigator. * History of systemic antimicrobials required for an infection within 7 days of first dose BI 765049. * Patient with 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 * Presence of hepatitis C-RNA * Patient with known human immunodeficiency virus (HIV) infection. * Patient previous treatment history: * 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. * Treatment with extensive field radiotherapy including whole brain irradiation within 14 days prior to first administration of BI 765049. * Further exclusion criteria apply