A Study in People With Advanced Cancer (Solid Tumours) to Test Different Doses of BI 3810944 and to Find Out Whether it Helps

Inclusion Criteria: 1. Trial participant population specifically to Part A and B: * Part A only: participants with any histologically or cytologically confirmed diagnosis of solid tumour who failed conventional treatment or for whom no therapy of proven efficacy exists or who is not eligible for established treatment options. Participant must have exhausted available treatment options known to prolong survival for their disease. * Part B only: participants with histologically or cytologically confirmed diagnosis of who has progressed on, or is intolerant to available standard therapies, or for whom no standard therapy with proven benefit exists according to the local and institutional guidelines. Participants should not have received \>3 previous lines of treatment (excluding prior systemic regimens received at adjuvant or neoadjuvant setting and excluding treatment with tumour-infiltrating lymphocytes at any timepoint). B-raf protein kinase (BRAF) mutation status must be known prior to screening 2. Eastern cooperative oncology group (ECOG) performance status of 0 or 1 3. Presence of at least one measurable lesion outside of central nervous system (CNS) as defined per response evaluation criteria in solid tumours (RECIST v 1.1) 4. Age ≥18 years 5. Adequate organ function 6. Life expectancy of ≥3 months at the start of the trial treatment in the opinion of the investigator 7. All toxicities related to previous anticancer therapies have resolved to common terminology criteria for adverse events (CTCAE) Grade ≤1 prior to trial treatment administration (except for alopecia and peripheral neuropathy which must be CTCAE Grade ≤2 and amenorrhea/menstrual disorders which can be any Grade) Further inclusion criteria apply. Exclusion Criteria: 1. Active primary central nervous system (CNS) malignancy, active untreated CNS metastases and/or carcinomatous meningitis * Participants with asymptomatic (i.e. no clinical neurological symptoms) brain lesions are eligible provided they meet the following criteria: * Radiotherapy or surgery for brain metastases was completed ≥2 weeks before the first administration of BI 3810944 * Patient is off steroids for ≥7 days (physiologic doses of steroids are permitted), and the patient is off anti-epileptic drugs for ≥7 days or on stable doses of anti-epileptic drugs for malignant CNS disease 2. A diagnosis of immunodeficiency; receiving chronic systemic therapy exceeding prednisone 10 mg daily or equivalent or any other form of immunosuppressive therapy within 7 days before the first dose of BI 3810944 3. Prior anticancer therapy: * Participants who have been treated with any other anticancer drug(s), within 28 days or within 5 half-life periods (whichever is shorter) prior to the first administration of BI 3810944 * Participants who have been treated with extensive field radiotherapy including whole brain irradiation, within 2 weeks prior to first administration of BI 3810944 4. Prior treatment with organ transplant or hematopoietic stem-cell transplant 5. Anticoagulant treatment that cannot be safely interrupted based on opinion of the investigator if medically needed (e.g. biopsy) 6. Women who are pregnant, breastfeeding or who plan to become pregnant or breastfeeding during the trial or within 4 months after the last dose of BI 3810944 Further exclusion criteria apply.