I can logon to as many AIM screennames as I want to by a process where I "clone" the AIM client. It requires hex editing the aim.EXE file, though. I have ten aim clients set up in folders AIM1, AIM2, AIM3, etc. I may be able to send the already hexed EXE's to you if you want to go this route (you need AIM 4.7)
The number of AIM clients you can have running is limited by your systems ability (resources, memory, etc) and perhaps a cap on the number of AIM connections that AIM will allow you to have from your internet address.