A Study to Test Whether Treatment With BI 770371 in Combination With Pembrolizumab With or Without Cetuximab Helps People With Head and Neck Cancer Compared With Pembrolizumab Alone

Inclusion Criteria: * Patients with histologically confirmed metastatic or recurrent HNSCC of the primary tumour location of oral cavity, oropharynx, hypopharynx, and larynx not amenable to locoregional treatment with curative intent. * Willingness to provide pretreatment (baseline) biopsy/tissue to the sponsor (fresh or archival one). A newly obtained biopsy is preferred but an archival sample is acceptable, with tumor tissue (formalin fixed paraffin embedded \[FFPE\] block preferred, or at least 10 freshly sectioned unstained FFPE slides) from a core or excisional biopsy. Any deviation from this rule requires approval by the sponsor. Details on the requirements for archival tumour tissue and on biopsy sample collection are provided in the Laboratory Manual. * Patients who have not received prior systemic treatment for metastatic or recurrent HNSCC. Systemic therapy (including cetuximab) which was completed more than 6 months prior to progression of disease if given as part of multimodal treatment for locally advanced disease is allowed. * Patients who do not have contraindications to pembrolizumab monotherapy according to pembrolizumab local label, guidelines, treatment standards, regulations or the document (label of another country if pembrolizumab local label is not available) provided in the investigator site file (ISF) by the sponsor. * Patients who do not have contraindications to treatment with cetuximab according to cetuximab local label, guidelines, treatment standards, regulations, or the document (label of another country if cetuximab local label is not available) provided in the ISF by the sponsor. * Presence of at least one measurable non-central nervous system (CNS) lesion (according to RECIST v1.1.). * Further inclusion criteria apply. Exclusion Criteria: * Nasopharyngeal carcinoma (NPC) of any histology, primary tumour location at nasal cavity, paranasal sinuses of any histology, any cancer of unknown primary. * Any tumour location necessitating an urgent therapeutic intervention (e.g., palliative care, surgery, or radiation therapy), such as spinal cord compression, other compressive mass, uncontrolled painful lesion, bone fracture. * Patients with progressive HNSCC within 6 months of completion of systemic therapy for locoregionally advanced disease with curative intent. * Receiving treatment for brain metastases or leptomeningeal disease (LMD) which may interfere with safety and/or endpoint assessment. Patients with previously diagnosed brain metastases are eligible if they have completed their treatment and have recovered from the acute effects of radiation therapy or surgery prior to trial entry, have discontinued corticosteroid treatment for these metastases and are clinically stable, off anticonvulsants for at least 4 weeks and are neurologically stable before enrollment. * Patients for whom single agent pembrolizumab is not the preferred treatment (e.g. patients for whom chemotherapy or anti-PD-1 in combination with chemotherapy is considered the preferred therapy by the investigator or treating physician). * Prior treatment with any anti signal regulatory protein alpha (SIRPα) or anti-integrin-associated protein (CD47) agent, regardless of treatment intent. * Prior cancer treatment with any anti PD-1 or anti PD-L1 agent or with an agent directed to another stimulatory or co-inhibitory Tcell receptor (e.g. CTLA-4, OX 40, CD137), regardless of treatment intent. * Prior allogeneic stem cell or solid organ transplantation. * Further exclusion criteria apply.