and have them point to the same environment? I know this works when I got to the IP address of a system as well as that system's vanity url. I'm not sure, however, if that is production-safe or just happens to work for me. Assuming you sign in with the same user, you'd always be signing in to the same application, but at least you don't have to have multiple browsers.
Also, I wonder if there's some fancy footwork that can detect the URL on sign in and attempt to switch the access group to that application if the user has it. You'd have to security this activity very carefully to make sure injecting an access group would be impossible.