Sessions won't help you either, at least not by themselves.
The only thing you can do for multisite logins is to have ownership of both sites, and either share a database or have one site query another for information through something like soap or rest or whatever. Cookies cannot be shared between two sites (although they can be shared with subdomains). When the request is received which will need to use the GET for the phpsessid, than it should process it per normal on either site. If they share the same filesystem or database, then you can use the session information on either site.
header('HTTP/1.1 420 Enhance Your Calm');