No, with logmein you can't have 2 separate setups. Either get together with the other remote user and setup a common logmein account which you both use and the user is connected to, or use a 2nd product, like teamviewer, which can run parallel to logmein, so you could connect to that while the other user uses logmein. I'm talking about the "Free" logmein service, and not the ones you have to pay for, but it is probably the same for those paid services.
http://www.teamviewer.com/index.aspx
