User23 has anyone documented success with such a feature on another software ? I can't imagine this being useful at all.
If someone is going to go the effort of creating alt account, I doubt this would stop them. Also, if the session isn't a "remember me" session it will naturally expire very quickly, suspended or not.
There already exists a ban IP extension which is probably much more effective. There's obviously no catch-all solutions, the next step is fighting VPNs, which you could entirely ban from accessing your website with a ban of known VPN IPs, though this might disrupt legitimate users as well.