I find I can handle multiple chats at once easily using programs like TextExpander(Mac) or Breevy(Win).

That way, if someone needs a specific walkthrough, I can type something like oguide and it automatically pastes this link: https://www.olark.com/help/guide

Then if you model your support system around making the walkthroughs and guides for the most common user issues, it makes juggling chats much easier.