When I open Mission Control, I see that I can drag windows between Spaces and that moves the window to that Space.
What I want is to copy the window instance so I can interact with it on any of the Spaces.
This is very common functionality for virtual desktop programs on Windows (like Dexpot), where for example I can have my email program always available as I move around to different desktops. I'd like to do this same thing with Mission Control.
Best Answer
You can't get one window of an app to follow you to all Spaces - but you can, if you have shortcut keys setup to swap Spaces, grab the menu bar of the required window, hit the shortcut & 'take it with you' to the new Space.
If you don't have it set up already, System Prefs > Keyboard > Shortcuts…
One thing to note - if you do that with Finder windows, it can break the 'click desktop to go back to Space 1' functionality, til you relaunch the Finder.