You need to get all the way to the login screen before opening a 2nd CoH client. There are more complicated ways that allow you to bypass that.
Here's me with 4 Masterminds. For non-City of Hero players Masterminds are similar to Necromancers in Diablo 2 or any type of character that summons "Pets" or "Henchman" to do the work. All the characters with green names in the picture are me or my henchman.