It is possible and I am told a much more informal process than transferring into engineering from an outside program. Nothing is guaranteed, however. There needs to be space available, but I’m assuming a chat with the dean, might help…just sayin.
As for transferring into business, I’m afraid I know much less about that. I’d just call the College of Business and ask the all powerful undergraduate program coordinator for the program that she’d like to transfer into. They’re the ones who actually carry out the process of transfers and everything else for that matter when it comes to a given program.