Most of them do not appreciate being stopped on their way in unless it has been prearranged (as in if you are in touch with them some other way and they say "oh, meet me before the show").
If they're going out an alternate exit (of which there are at least two that I know of) it's because they do not want to stop for autographs. Trying to wait for them at one of those other doors (again, unless it's prearranged) just isn't nice or fair. Remember that stagedooring isn't a requirement on their part. Their job is over...if they want to go home let them.
"I wrote a book: "How to Be Popular". Now I've put together a top ten list of how to help you:
-Elphie, everyday... shower. I mean, who knows? Maybe some of that green is gonna come off!
-Deodorant Elphie. No body likes a stinky witch!
-I think we've covered the hair, we'll get to that.
-Clean underclothes. That's all I'm gonna say.
-Look at your posture. That's no way to be popular!
-Bed made, room straightened. We've done that.
-Colors blended. Oookay.
-But the most important thing to have, to make yourself popular, is to keep your beautiful smile."
~Kristin Chenoweth in her last performance of the song "Popular"