All Cohorts: - Male or female participants must be aged 6 to < 18 years of age at the time of signing the assent form and their caregiver signing the informed consent form. - Body weight greater than (>=) 15 kilograms (kg). EGPA Cohort: - Therapy with corticosteroids: The prescribed dose of oral corticosteroids (OCS) (greater than [>] 0.1 milligrams per kilogram per day (mg/kg/day), max dose of 50 milligrams per day (mg/day) must be stable (that is, no adjustment of the dose) for at least 4 weeks prior to baseline (Visit 2). - Immunosuppressive therapy: If receiving immunosuppressive therapy, the dosage must be stable for at least 4 weeks prior to baseline (Visit 2). HES Cohort: - Documented HES diagnosis, defined as history of persistent eosinophilia >1500 cells/µL without secondary cause on 2 examinations ≥1 month apart and evidence of eosinophil-mediated organ involvement. - Symptomatic active HES, or history of a prior flare, or considered eligible based on disease severity per investigator judgement. - AEC ≥1000 cells/µL at screening (Visit 1). - Documented negative testing for Fip1-like 1 gene fused with the platelet-derived growth factor receptor alpha gene (FIP1L1-PDGFR) fusion tyrosine kinase gene translocation.

All Cohorts: - Any current malignancy or history of malignancy. - History of anaphylaxis to any biologic therapy or vaccine. - Known, pre-existing, clinically significant endocrine, autoimmune, metabolic, neurological, renal, gastrointestinal, hepatic, haematological, respiratory, or any other system abnormalities. - Previous receipt of benralizumab in an interventional clinical study. EGPA Cohort: - Diagnosed with granulomatosis with polyangiitis (previously known as Wegener'granulomatosis) or microscopic polyangiitis. - EGPA relapse: any deterioration in EGPA and/or organ-threatening EGPA that per Investigator judgement renders participants unstable in their EGPA within 3 months prior to screening (Visit 1) and through first administration of IP at baseline (Visit 2). - Life-threatening EGPA: imminently life-threatening EGPA disease within 3 months prior to screening (Visit 1) and through first administration of IP at baseline (Visit 2), as per Investigator judgement. HES Cohort: - Life-threatening HES or HES complications, as judged by the investigator. - Hypereosinophilia of unknown significance (HE-US). - Diagnosis of systemic mastocytosis.