Yes, this is possible.  This actually how we started our IFS V8 setup and then retained that through V9.  We had one set of profiles for the UK company, then created a copy of each profile for the US company.  However, we very quickly found that this was a lot of work to maintain and when we went live with the third company, we had started to undo the separation we had initially.  Now that we have taken the fourth company live, we are now in the process of actively combining the permissions across all companies to be uniform and there are only two global profiles that everyone will use.  We are moving away from the separate base profiles because it has been a lot of overhead work to maintain them all.  But if there is an absolute business reason for them to be different, it is certainly possible.