This Study Aims to Find and Test a Safe Dose of BI 905677 in Patients With Different Types of Cancer (Solid Tumours)

Inclusion criteria * Histologically or cytologically confirmed diagnosis of an advanced, unresectable and/or metastatic non-haematologic malignancy. Patient must have measurable or evaluable lesions (according to Response Evaluation Criteria in Solid Tumours (RECIST) 1.1). * Patient who has failed conventional treatment or for whom no therapy of proven efficacy exists or who is not eligible for established treatment options. Patient must have exhausted treatment options known to prolong survival for their disease. * Patient willing to undergo mandatory skin biopsy at the timepoints specified in the protocol. * Eastern Cooperative Oncology Group score of 0 or 1. * Adequate organ function defined as all of the following: * Absolute neutrophil count (ANC) ≥ 1.5 x 109/L; haemoglobin ≥ 9.0 g/dL; platelets ≥ 100 x 109/L without the use of hematopoietic growth factors within 4 weeks of start of study medication. * Total bilirubin ≤ 1.5 times the upper limit of normal (ULN), except for patients with Gilbert's syndrome: total bilirubin ≤ 3 x ULN or direct bilirubin ≤ 1.5 x ULN. * Creatinine ≤ 1.5 x ULN. If creatinine is \> 1.5 x ULN, patient is eligible if concurrent creatinine clearance ≥ 50 ml/min (measured or calculated by CKDEPI formula or Japanese version of CKD-EPI formula for Japanese patients). * Aspartate transaminase (AST) and alanine transaminase (ALT) ≤ 3 x ULN if no demonstrable liver metastases, or otherwise ≤ 5 x ULN * Alkaline Phosphatase \< 5 x ULN * Recovered from any previous therapy-related toxicity to ≤ Common Terminology Criteria for Adverse Events (CTCAE) Grade 1 at start of treatment (except for alopecia and stable sensory neuropathy which must be ≤ CTCAE Grade 2). * At least 18 years of age at the time of consent or over the legal age of consent in countries where that is greater than 18 years. * Signed and dated written informed consent in accordance with ICH-GCP and local legislation prior to admission to the trial. * Life expectancy ≥ 3 months at the start of treatment in the opinion of the investigator. * Male or female patients. Women of childbearing potential (WOCBP) must only be included after a confirmed menstrual period within the past 4 weeks and a negative pregnancy test at screening. WOCBP with irregular menstruation may be included after two negative pregnancy tests during screening between 2 and 4 weeks apart. WOCBP and men who are able to father a child must be ready and able to use highly effective methods of birth control, per ICH M3 (R2), that result in a low failure rate of less than 1% per year when used consistently and correctly. These methods must be used during the study and for at least 6 months after the last dose of BI 905677. A list of contraception methods meeting these criteria is provided in the patient information. Exclusion criteria * Major surgery (major according to the investigator's assessment) performed within 4 weeks prior to first trial treatment or planned within 6 months after screening. * Previous or concomitant malignancies other than the one treated in this trial within the last 2 years, except; * effectively treated non-melanoma skin cancers * effectively treated carcinoma in situ of the cervix * effectively treated ductal carcinoma in situ * other effectively treated malignancy that is considered cured by local treatment * Osteoporosis ≥ Common Terminology Criteria for Adverse Events (CTCAE) Grade 2 * Chronic corticosteroid use * Osteoporotic compression fracture within 12 months prior to informed consent which is clinically significant in the opinion of the investigator. * Patients who must or wish to continue the intake of restricted medications or any drug considered likely to interfere with the safe conduct of the trial. * Previous treatment in this trial. * Treatment with a systemic anti-cancer therapy or investigational drug within 28 days or 5 half-lives (whichever is shorter) of the first treatment with the study medication. * Any history of or concomitant condition that, in the opinion of the investigator, would compromise the patient's ability to comply with the study or interfere with the evaluation of the safety and efficacy of the test drug. * Women who are pregnant, nursing, or who plan to become pregnant or nurse during the trial or within 6 months after the last dose of study treatment. * Active alcohol or drug abuse in the opinion of the investigator. * Patient unwilling or unable to comply with the protocol. * Presence or history of uncontrolled or symptomatic brain or subdural metastases, unless considered stable by the investigator and local therapy was completed. Inclusion of patients with newly identified brain metastasis/es at screening will be allowed if patients are asymptomatic. * Known history of human immunodeficiency virus (HIV) infection or an active hepatitis B or C infection which in the opinion of the investigator may interfere with participation in the trial. * History of severe hypersensitivity reactions to monoclonal antibodies. * History of allergy to kanamycin or similar class drugs (including streptomycin, gentamicin, amikacin, tobramycin and neomycin).