SSO relies on a common directory of users. Cloud systems have their own internal system which you can't connect up to other servers. So I'm afraid the answer is "no".
You might be able to code something that can take the Cloud authentication tokens and duplicates the process for logins for other systems, but I don't think it would be easy, and I've a nagging doubt that it would be very insecure, as well as add a "duplicate all users in two systems" overhead.
For JSM June Challenge #2, share how your non-technical teams like HR, legal, marketing, finance, and beyond started using Jira Service Management! Tell us: Did they ask to start using it or...
Connect with like-minded Atlassian users at free events near you!Find an event
Connect with like-minded Atlassian users at free events near you!
Unfortunately there are no Community Events near you at the moment.Host an event
You're one step closer to meeting fellow Atlassian users at your local event. Learn more about Community Events