A feature to move running apps between different graphical sessions

I would love to see a feature on Wayland or xorg, that would allow for a running application to move from one graphical server to another, if the user has permissions for that.

I know this is tricky. But it would be super useful.

Imagine is a user has his desktop running and fully loaded with apps, and then it uses ssh or nxclient to connect to that machine.
The user would be able to list all graphical apps running under his id in any display servers are running on that machine.
It would then be possible run some command to transfer the output of a certain app to your current display server.
When the user is done with the app, the app should return to the original display server.

All of this would work without ever having to close or restart the app.

Sweet dreams :)