I suppose if you were to have multiple B.Net accounts, you can have an authenticator on each account.
If it was the same authenticator, like I have for my current 5 accounts, you'd likely have the same log in issues.
If it was a different authenticator per account, you'd have to enter a number on each authenticator (ie not broadcast/keyboard repeat), but there wouldn't likely be a 2.5 minute log in process either.