Assign to Specific Members of a Role

The way we wish to set up the Support Ticketing system is to have our locations as the clients and then assign only those at a location (based on role) to that client. With that said, is there a way to eliminate the Admins from showing up in the Assigned section?

Also, is there a way to only specify certain individuals to show up in that list?

Any help you can provide is appreciated!