Why would you want to?
The session ID is nothing but a hash key for sessions. From the way the docs read, the actual session map is common to the entire
Tomcat container, not one session map per Context. Which probably has to do with the fact that there is an option that permits a session to be shared across multiple webapps. So I can see where things would get messy if apps didn't have a common ID format.
The secret of how to be miserable is to constantly expect things are going to happen the way that they are "supposed" to happen.
You can have faith, which carries the understanding that you may be disappointed. Then there's being a willfully-blind idiot, which virtually guarantees it.