Could you clarify? What about the cookies or session would you want to use for either identifying cached information or for storing in the cache?
You can always cache more than just the content returned by a response. You could have a filter save multiple files in your cache, say one for content, one for session information, etc. However, you will have to have a creative method for figuring out what cache information to use. Perhaps something along the lines of loading user-specific cache information when they log in, or by detecting a cookie you've saved on their machine.