Yes, you can use StartingNodeUrl. Basically, you set the url of the parent page of all your pages you want in the menu. The menu is then built using those pages and it doesn't change regardless of the page you are on.
I built a mojoPortal module for this a while back. You can see it here. You can login with email@example.com, password is admin.
If you're interested in purchasing it ($25), let me know.