No, this is currently not possible.
If you log in a second time with the same credentials, the session associated with the first login is deleted.
I'd imagine this is probably because a session cookie is created for the Firefox profile you first log in with, when you log in again with a different Firefox instance the session cookie is shared providing the same profile is being used. You should be logged out if you create a new session from an instance of Firefox with a different profile set, or a instance of Firefox on a different machine.
Ok, I just tested this but I've pressed a 'new' button in three times in three different instances of Firefox with the same named user account.
The only time I was actually logged out by the system was when I used that user account in Internet Explorer (then all three Firefox instances were logged out)...