Tue Sep 28, 2010 2:25 pm by ShadowKntSDS
This is only an issue with trial accounts. You can have as many different regular account clients running as you'd like. In fact CCP encourages this by offering special discounts occasionally for people to get a 2nd account.
If you have a trial account logged in, you can not have any other EVE account logged on the same machine.
The reason this is not allowed with trial accounts is that EVE has a lot of meta gaming going on, and there are repressions for your actions. If you could just roll as many trial account alts as you want, and have them all online at the same time, you could very easily have real time spys all over the universe. Additionally, you could muster up a strong enough for to take down almost anyone in secure space without having any of the consequences to your security rating or outlaw status.