Maintain anonymous conversation after anonymous's disconnect?

Is it possible to log in anonymously, chat with a recipient, log out, then log back in as the same anonymous user in XIFF? I have a potential goal of placing a chat support feature on a website, on every page. When the user moves from one page to the other, I want to continue the conversation where it left off, using the same ID. That way the support staff member will not go crazy while several chat windows open as the visitor of the website moves from page to page. As a last resort, I could have Flash get session information from page to page and just pass the basic user info in a new chat window as starter chat (but on every page ikk!). Any thoughts? I’ll keep digging.

Thanks much in advance.