Troll the Trolls
Agree with the stated VPNs. Also email addresses are virtually endless and free.
What's more telling is writing styles and patterns used. Its almost like a fingerprint for some people.
I have a member on my forum that has a second account. IPs different as are the email address when looking into the forums APC to verify but the writing style and patters are a dead giveaway.
If everyone would just ignore what this guy posts and not ever once comment on it, he would grow tired of non attention and go elsewhere. But as soon as you feed the troll, he grows hungry and wants more and more.
As a side note: When I owned a vBulletin forum platform there was a great plug in that I used on trolls. I forget the exact name of it now but what you did is install the plug in and it created it's own user group in vB. Then you assigned said troll as a secondary member of this user group. What that did is make it so the troll had a one in ten chance of getting logged on, posting anything, PMing someone, clicking on a thread, just about everything they did would end in a redirect to no where, give them an error message, fail to post their post, basically drive them crazy. It was the best way to troll a troll as you turned the tables and just utterly frustrated them till they quit.
Another really great one I used too was I think called "global ignore". Again another plug in I installed and it created a secondary user group to put your trolls in. What this did is put them on everyone's ignore list except admins and mods. All their threads, posts, PMs to people except admins and mods would be invisible. All their BS trolling never got a single comment as they were never seen by the membership, only the admins and mods and of course themselves. it's like they were sitting in an empty room all by them selves. "...hello?... hello?...anyone here?"
These two plug ins were a million times more enjoyable to just put the trolls in and let them go crazy. Rather then you having to chase after them and IP address which are no longer helpful..... vBulletin is a great platform for that kind of stuff and I will say as an admin owning and running a board these people are just terrible as we all know they drive you and everyone else crazy but by putting them in these secondary usergroup and letting them go crazy instead was just so rewarding! :rofl