A Comprehensive Multiomic Biomarker Evaluation Across Two Single-arm Cohorts to Elucidate Mechanisms of Response and Resistance in Recurrent/Metastatic (R/M) Head and Neck Squamous Cell Carcinoma (HNSCC)

Inclusion Criteria: 1. Written informed consent 2. At least 18 years old at the time of signing Informed Consent Form (ICF). 3. Histologically or cytologically confirmed Head and Neck Squamous Cell Carcinoma (HNSCC) with evidence of metastatic or locally recurrent/advanced disease not amenable to curative local therapy (surgery or radiation). Eligible primary tumor locations include oral cavity, oropharynx (p16 positive or negative), hypopharynx and larynx. Patients with unknown primary HNSCC, SCC of nasopharynx or paranasal sinuses are excluded. 4. For oropharyngeal cancer, documented Human Papillomavirus (HPV) status (p16 Immunohistochemistry (IHC) or HPV DNA/RNA) is required. 5. At least one measurable lesion per RECIST v1.1 6. ECOG performance status of 0 or 1. 7. Life expectancy greater than 12 weeks. 8. Cohort-Specific Criteria: * Cohort A: R/M HNSCC in the second- or third-line setting, pretreated with an Immune Checkpoint Inhibitor (ICI) and progressed on platinum-based therapy in the R/M setting. * Cohort B: R/M HNSCC in the first-line setting, systemic therapy-naïve in the R/M setting. 9. Willingness and ability to undergo both a newly obtained, image-guided or surgical tumor biopsy during the screening period and a mandatory on-treatment tumor biopsy. 10. No evidence of past or active hepatitis B infection, w/exception 11. No evidence of active hepatitis C infection. Patients with undetectable Hepatitis C Virus (HCV) Ribonucleic Acid (RNA) test are eligible. 12. Participants must have no known history of HIV infection. HIV-1/2 testing is only required for patients with known risk factors. 13. Willingness and ability to comply with scheduled visits, treatment plans, laboratory tests, and other protocol requirements. 14. Patients with feeding tubes (e.g. gastrostomy tubes) are eligible. 15. Patients must have adequate organ function, as defined in protocol 16. A female participant is eligible to participate if she meets all the criteria listed in protocol 17. Male participants are eligible to participate if they agree to criteria listed in protocol during the study intervention period and for at least 5 months after the last dose of GSK5764227. Exclusion Criteria: 1. Participants with non-squamous histologies (e.g., adenocarcinoma, salivary gland carcinomas, and sarcomas) or HNSCC arising from the nasopharynx or paranasal sinuses are excluded. Participants with unknown primary tumors (even if squamous histology is confirmed) are also excluded. 2. Has ongoing adverse reaction(s) from prior therapy that have not recovered to ≤Grade 1 or to the baseline status preceding prior therapy (excluding, for example, alopecia, hearing loss, vitiligo, endocrinopathy managed with replacement therapy, and Grade 2 neuropathy), or that the Investigator, with the agreement of the Study PI, considers to be not clinically relevant for the tolerability of study intervention in the current clinical study. 3. Any participation in another investigational study within 4 weeks prior to screening. 4. Prior treatment with orlotamab, enoblituzumab, I-Dxd, or other B7-H3 targeted agents. 5. Has a history of autoimmune disease that has required systemic treatments in the 2 years prior to screening. \- For dostarlimab: Patients requiring chronic systemic immunosuppressive therapy within 30 days prior to first dose are excluded, except for those receiving low-dose corticosteroids (≤10 mg/day prednisone equivalent), inhaled/topical steroids, or physiological replacement therapy. 6. Serious arteriovenous thromboembolic events (such as deep vein thrombosis, pulmonary embolism, etc.) within 3 months prior to the first dose (w/exceptions) 7. Evidence of brain metastasis unless all the following criteria are met: * Asymptomatic. * Medically stable for at least 4 weeks prior to initial dosing. * No steroid treatment required for at least 2 weeks prior to initial dosing. * No imaging evidence of severe edema located around the tumor lesion. * Also excluded are untreated progression due to brain metastasis during or after the last treatment prior to screening, evidence of meningeal/brainstem metastasis, or evidence of spinal cord compression (detected by radiographic examination, symptomatic or not). 8. History of another primary solid tumor except for the following: * Solid tumors that have been cured and inactive for ≥2 years before enrollment and at very low risk of recurrence. * Prior HNSCC primary that has been curatively treated with no evidence of disease at enrollment. * Adequately treated non-melanoma skin cancer or lentigo maligant without evidence of relapse. * Adequately treated carcinoma in situ (e.g., cervix carcinoma in situ) without evidence of relapse. * Definitively treated non-metastatic prostate cancer. 9. Has had any major surgery (such as craniotomy, thoracotomy, or laparotomy) within 4 weeks prior to first dose of study intervention. 10. History of prior allogeneic or autologous bone marrow transplant or solid organ transplant. 11. Any of the cardiac examination abnormalities as listed in protocol. 12. Serious or poorly controlled hypertension, including history of hypertensive crisis, hypertensive encephalopathy, adjustment of antihypertensive medications due to poor blood pressure control within 2 weeks prior to the first dose, or recurrent systolic blood pressure ≥160 mmHg or diastolic blood pressure ≥100 mmHg during the screening period. 13. Clinically significant bleeding symptoms or significant bleeding tendency within 1 month prior to the first dose, and: * Receipt of any transfusion of blood products (including platelets or red blood cells) or administration of colony-stimulating factors (including G-CSF, granulocyte-macrophage colony-stimulating factor, or recombinant erythropoietin) within 14 days before enrollment, and * Donation of blood or blood products more than 500 mL (approximately 1 pint) within 1 month prior to the first dose of study intervention. 14. Serious infections within 4 weeks prior to the first dose, including but not limited to the list in protocol. 15. Any history or current evidence of pulmonary disease 16. History of severe neurological or psychiatric disorder (including, but not limited to, epilepsy, dementia, or major depression) or any serious and/or unstable medical, psychiatric, or other condition (including laboratory abnormalities) that, in the Investigator's judgment, could interfere with the participant's safety, ability to provide informed consent, protocol compliance, or the assessment of study outcomes. 17. Has any active renal condition (e.g., requirement for dialysis, or any other significant renal condition that could affect the participant's safety). 18. Allergy or hypersensitivity to any component of GSK5764227 (ADC, antibody, toxin GSK5757810); history of severe allergies (e.g., anaphylactic shock) or severe infusion-related reactions; or idiosyncrasy to recombinant humanized or mouse proteins. For Cohort B, this also includes allergy or hypersensitivity to dostarlimab or any of its components. 19. Receipt of live vaccine within 30 days of the start of study intervention. 20. Has any condition that jeopardizes the safety of the patient or interferes with the assessment of the study, as judged by the Investigator. 21. Any of the following hepatic conditions: * Current hepatic encephalopathy, hepatorenal syndrome, or Child-Pugh Class B or more severe cirrhosis. * Cirrhosis or current unstable liver or biliary disease per Investigator assessment, defined by the presence of ascites, encephalopathy, coagulopathy, hypoalbuminemia, esophageal/gastric varices, or persistent jaundice. o Note: Stable noncirrhotic chronic liver disease (including Gilbert's syndrome or asymptomatic gallstones) or hepatobiliary involvement of malignancy is acceptable if the participant otherwise meets entry criteria. * Documented presence of HBsAg, HBcAb, or HBsAb (except when HBsAb is attributable to previous vaccination) at screening or within 3 months prior to the first dose of study intervention. * Positive HCV antibody test result at screening or within 3 months prior to the first dose of study intervention. o Note: Participants with a positive HCV antibody test result due to prior resolved disease may be enrolled if a confirmatory negative HCV RNA test is obtained and the participant otherwise meets entry criteria. * Positive HCV RNA test result at screening or within 3 months prior to the first dose of study intervention. * Note: The HCV RNA test is optional; participants with a negative HCV antibody test are not required to undergo HCV RNA testing. 22. Has received prior anticancer therapy and has not completed a washout period of at least 5 half-lives or 28 days, whichever is shorter, prior to the first dose of study intervention, or requires continued use these medications during the study. 23. History of local palliative radiotherapy within 2 weeks prior to the first dose of study treatment. Extensive field radiotherapy requires a washout of 4 weeks prior to the first dose of study treatment. 24. Concurrent use of the following medications within 7 days prior to the first dose of study intervention, or need to continue during the study