Do you also have multiple accounts for Skype or any other mac app? For example if you've got a private and a business account. You can't login with two accounts in the same Skype instance. What you can do instead is starting a second instance of the app. All you need to have is a second mac user. If you've got root access you can simply use the root user for that.
On your console just run the app with the path to your app:
$ sudo /Applications/Skype.app/Contents/MacOS/Skype