I never get that. Do you want to be in engineering or business?
Nonetheless, no can do given it is not a direct admit school. To OP, I recommend you choose major over school name. In engineering, the school name matters little. ABET accreditation matters. Don’t go to school for something that isn’t what you want to study - in my opinion.
Myriad accredited schools will be safe and budget friendly thanks to your achievements.
From W&M - Students must apply directly to the Mason School if they wish to major or minor in a business discipline, typically during the second semester of sophomore year due to prerequisites required within the undergraduate program.