Can I create a common domain user and associate it with other domain users?

I need a common domain user that can be used by multiple people. These people have their own domain user accounts. They should be able to login to a machine using the common domain user account, but at the same time their original identity should also get logged/authenticated. This is something like a group. But i need it to be a user so that when they login to a machine, separate user profiles are not created for each of them. Is it possible to achieve this in some way?

First, a common login is not a great security idea, but I do realize that some companies user them. If they do log in as that common user, short of a security camera, or file monitoring software, you are not going know who logged in…To a computer and domain, they ARE that common domain account.

A better idea is just to have them log in with their domain accounts to that computer, and if you need to set up a common set of programs, just make sure they are copied to the default user before the users log in for the first time, so they get those settings.