A Study to Test Different Doses of BI 764532 in Patients With Small Cell Lung Cancer and Other Neuroendocrine Tumours That Are Positive for DLL3

Inclusion Criteria: * Signed and dated, written informed consent form (ICF2, ICF3 or ICF4) in accordance with International Council for Harmonisation of Technical Requirements for Pharmaceuticals for Human Use (ICH) - Good Clinical Practice (GCP) and local legislation prior to any trial-specific procedures, sampling, or analyses. * Locally advanced or metastatic cancer not amenable to curative treatment; of following histologies: * Small cell lung carcinoma (SCLC) * Large cells neuroendocrine lung carcinoma (LCNEC) * Neuroendocrine carcinoma (NEC) or small cell carcinoma of any other origin * Tumours must be positive for DLL3 expression (on archived tissue or instudy fresh biopsy) according to central pathology review in order to start BI 764532 * Patients with tumours with mixed histologies for any above type are eligible only if neuroendocrine carcinoma/small tumor cells component is predominant and represent at least 50% of the overall tumour tissue. * For back-fill cohorts only: patient has agreed to and signed an IC to provide mandatory pre-treatment and on-treatment fresh tumor biopsy. * Patient has failed or is not eligible for available standard therapies according to local guidelines. Standard therapies should include at least one line of chemotherapy that should include platinum for patients with small cells carcinoma tumors histologies. * Eastern Cooperative Oncology Group (ECOG) performance status of 0-1. * At least one evaluable lesion outside of CNS as defined per modified Response Evaluation Criteria In Solid Tumors (RECIST) 1.1 * Subjects with brain metastases are eligible provided they meet the following criteria: * Radiotherapy or surgery for brain metastases was completed at least 2 weeks prior to the first administration of BI 764532 * Patient is off steroids for at least 7 days (physiologic doses of steroids are permitted), and the patient is off anti-epileptic drugs for at least 7 days or on stable doses of anti-epileptic drugs for malignant Central Nervous System (CNS) disease. * Adequate liver, bone marrow and renal organ function Further inclusion criteria apply. Exclusion Criteria: * Previous treatment with T cell Engager (TcE) or cell therapies targeting DLL3. Other DLL3 targeting agents (like Rovalpituzumab tesirine (RovaT)) are allowed only if DLL3 positivity is documented after completion of treatment with DLL3 targeting agent in post-treatment biopsy. * Anticoagulant treatment that cannot be safely interrupted based on opinion of the investigator if medically needed (e.g. biopsy). * Persistent toxicity from previous treatments that has not resolved to = Common Terminology Criteria for Adverse Events (CTCAE) Grade 1 (except for alopecia, CTCAE Grade 2 neuropathy, asthenia/fatigue or grade 2 endocrinopathies controlled by replacement therapy). * Patient has a diagnosis of immunodeficiency or is receiving systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to the first dose of BI 764532. Physiological replacement of steroids is allowed. * Prior anti-cancer therapy: * Patients who have been treated with any other anti-cancer drug within 3 weeks or within 5 half-life periods (whichever is shorter) prior to first administration of BI 764532. * Patients who have been treated with extensive field radiotherapy including whole brain irradiation within 2 weeks prior to first administration of BI 764532. * Other active malignancy that could interfere with the prognosis and treatment of the disease of the study. * Major surgery within 28 days of first dose BI 764532. * Women who are pregnant (including those who are considered to be possibly pregnant based on the investigator's clinical judgement), nursing/breast feeding or who plan to become pregnant or nurse while in the trial or within 35 days after the last dose of study treatment. * Active infection that requires medical therapy or other clinically significant intervention or within 2 weeks prior to study entry confirmed (PCR test or other applicable test as per local requirements) or suspected SARS-CoV-2 infection or close contact with an individual with confirmed SARS-CoV-2 infection. Further exclusion criteria apply.