There are many ways to share data between processes. You can use a local dbm file. You can use IPC::Shareable. And so on. But all of the efficient ones have the rather significant problem that all of the requests in your series have to come back to the same physical machine. This does not play well with load balancing.

However one crazy way of doing it is like this. One machine gets the request and forks off a local server. Other CGI requests are passed the necessary information to be able to access this temporary server, which is run in a persistent process, and then when this server decides the time is right, it de-instantiates itself. This would be a lot of work though.

Personally I would just see if you can keep the temporary state in the database, and just have each individual request deal with the bit of the state that they need to handle. But I cannot, of course, offer any guesses on whether this would work without knowing more details than you have given us.