This study is open to adults with advanced extrapulmonary neuroendocrine cancer. The purpose of this study is to find out if a study medicine called obrixtamig plus standard chemotherapy (carboplatin and etoposide) improves survival when compared to standard chemotherapy (carboplatin and etoposide) alone. Obrixtamig is an antibody-like molecule that may help the immune system fight cancer. Another purpose of the study is to test a medical device being developed to measure levels of the tumour marker delta-like ligand 3 (DLL3).

Participants are put into 2 groups randomly, which means by chance. One group (treatment arm) receives obrixtamig and standard chemotherapy followed by obrixtamig alone for up to 3 years. The other group (control arm) receives standard chemotherapy without obrixtamig for about 4 months. All treatments are given as infusions into a vein.

During the study, participants in both groups visit the study site regularly. Participants in the treatment arm stay overnight at the study site following the first 2 obrixtamig treatments. The doctors regularly check participants' health and take note of any unwanted effects. At some of the visits, doctors check the size of the tumour(s). The results are compared between the 2 groups to see whether the treatment works.

Inclusion Criteria:

1. Patients with poorly differentiated unresectable locally advanced or metastatic extrapulmonary neuroendocrine carcinoma (epNEC) with Ki-67 >20% or mitotic rate mitotic rate with number of mitoses >20 per 2 mm2, regardless of primary site (including site of unknown origin)
2. Patients with tumours with mixed histologies are eligible only if neuroendocrine carcinoma component is predominant and represents more than 70% of the overall tumour tissue
3. No prior systemic treatment for unresectable locally advanced or metastatic epNEC (except for the completed one cycle of standard platinum + etoposide). Prior peri-operative chemotherapy or -radiation for curative intention is allowed if at least 6 months have elapsed between completion of this therapy and diagnosis of unresectable locally advanced or metastatic disease
4. Patients who have finished one cycle of standard platinum + etoposide regimen as first-line treatment (Cycle 0: etoposide with carboplatin or cisplatin, administered at a minimum dose of cisplatin 75 mg/m2 or carboplatin area under the curve (AUC) 5 and etoposide 80 mg/m2) prior to randomisation
5. Patients must comply with criteria for receiving further chemotherapy treatment as first-line standard of care (SoC) treatment within 28 days after the start of the initial chemotherapy (Cycle 0)
6. Adequate archival Formalin-Fixed Paraffin-Embedded (FFPE) tumour tissue, as specified in the Laboratory Manual, must be available for central laboratory analysis of Delta-like ligand 3 (DLL3) expression status. Tumours must be positive (as defined in the diagnostic study protocol) for DLL3 expression status assessed by investigational VENTANA DLL3 (SP347) RxDx Assay
7. Eastern Cooperative Oncology Group (ECOG) score of 0 or 1
8. Male or female participants ≥18 years old and at least at the legal age of consent in countries where it is greater than 18 years at the time of signature of the informed consent form (ICF) Further inclusion criteria apply.

Exclusion Criteria:

1. Presence of leptomeningeal disease and/or carcinomatous meningitis
2. Patients with diagnosis of Merkel cell carcinoma or medullary thyroid carcinoma
3. Patients with neuroendocrine prostate cancer
4. Patients with well-differentiated neuroendocrine tumours of any grade according to the world health organization (WHO) classification, 5th edition
5. Patients with a history of well differentiated Neuroendocrine tumour (NET) tumour that transformed into poorly differentiated Neuroendocrine carcinoma (NEC)
6. Previous treatment with obrixtamig or other DLL3-targeting therapies (e.g. T-cell engager (TcEs), cell therapies, antibody-drug conjugates, or radiopharmaceuticals)
7. Previous treatment with anti-PD-1 or programmed death ligand 1 (PD-L1) therapies during the one cycle of standard platinum + etoposide first-line chemotherapy (Cycle 0)
8. Toxicity from previous treatments that has not resolved to ≤ Common Terminology Criteria for Adverse Events (CTCAE) Grade 1 or grade prior to Cycle 0. Participants with alopecia any grade, CTCAE ≤Grade 2 asthenia/fatigue, amenorrhea/menstrual disorders any grade, CTCAE ≤Grade 2 peripheral neuropathy, and/or CTCAE ≤Grade 2 endocrinopathies controlled by replacement therapy, and toxicities, which are considered irreversible but stable for at least 4 weeks, per Investigator judgement may be eligible Further exclusion criteria apply.

Once the criteria in section "Time Frame" are fulfilled, researchers can use the following link https://www.clinicalstudies.boehringer-ingelheim.com/msw/datasharing to request access to the clinical study documents regarding this study, and upon a signed "Document Sharing Agreement".

Furthermore, researchers can request access to the clinical study data, for this and other listed studies, after the submission of a research proposal and according to the terms outlined in the website.

One year after the approval has been granted by major Regulatory Authorities and after the primary manuscript has been accepted for publication, or after termination of the development program.

For study documents - upon signing of a 'Document Sharing Agreement'.

For study data - 1. after the submission and approval of the research proposal (checks will be performed by the sponsor and/or the independent review panel, including checking that the planned analysis does not compete with sponsor's publication plan); 2. and upon signing of a legal agreement.