Study to Evaluate Safety and Efficacy of Benralizumab in Subjects With Hypereosinophilic Syndrome

Background: \- Eosinophils are white blood cells that help fight infections. High eosinophil levels can damage people s organs, causing hypereosinophilic syndrome (HES). Researchers want to study if the drug benralizumab can help people with HES. Objective: \- To test if benralizumab can safely decrease eosinophils in people with HES. Eligibility: \- Adults age 18-65 who have been on stable HES therapy for at least 1 month but still have symptoms and high eosinophil levels. Design: * Participants will be screened with medical history, physical exam, and urine and blood tests. They will take simple heart and lung tests. * Participants will also have a bone marrow biopsy. A numbing medicine is injected into the outer covering of the bone. Then a needle is inserted into the bone. A fast suction movement takes bone marrow cells. * Phase 1: Participants will randomly receive either the study drug or placebo as an injection. * They will have daily visits for the next 3 days, then 4 weekly visits, and then 4 biweekly visits. Each time, they will have medical history, physical exam, blood tests, and a check of side effects. * They will receive another dose of the study drug or placebo at 1 month and 2 months after the first injection. * Phase 2 repeats the Phase 1 schedule. All participants will receive the study drug. * At 1 visit, participants will also receive a vaccine. At 4 visits, they will repeat the heart and lung tests. They will also have one other bone marrow biopsy. * After week 24, participants will receive the study drug either 6 times over 6 months or twice over 6 months.