Inclusion Criteria:

          -  Signed and dated, written informed consent form (ICF2) 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 Futher inclusion criteria apply

        Exclusion Criteria:

          -  Previous treatment with T cell Engager (TcE) or cell therapies targeting Delta-Like
             Ligand 3 (DLL3).

          -  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, nursing/breast feeding or who plan to become pregnant or nurse
             while in the trial or within 3 months 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 requirments) or suspected SARS-CoV-2 infection or close
             contact with an individual with confirmed SARS-CoV-2 infection.

        Further exclusion criteria apply