Overlay component with variants/boolean property


I’m have a little dropdown menu that will display different menu options depending on what item the user clicks.

So when i click button that opens the menu, and add the menu as the overlay, there is no way (that I can find) to set the boolean properties, is there?

And If I create different variants, suddenly I cannot use that component as a overlay (it will not show up in the list of possible overlays).

Is there a way to do this without having different components?