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I tried your suggestion. For simple geometry with very few dimensions and few or no projected edges, it is usable. However, in my opinion it can't replace my function proposal because I only managed to copy the geometry and sketch constraints this way. I wasn't able to copy the dimensions. It seems the relation for projected edges is lost, too. Maybe I made something wrong ?

One of the problems I'm trying to solve with this suggestion is that a sketch created by clicking on a part face is *forever* tied to this face. I can't assign it to another parallel face/plane. For instance: I have a stair. I want to make a feature on the first step but my sketch is tied to step N°3 by mistake -please note: this example is purposely simple, with complicated parts and sketches this happens much more insidiously-, I can't move and assign my sketch to the right step.

How it could work ?
maybe:
1° right click "move this sketch to..." on the sketch in the design explorer
2° little pop-up window. select the plane or face on the part. only the faces and planes which are applicable are selectable and highlighted with the mouse pointer. When selection is done click OK button.

However, I think you should rather take a look at how competitor products might have solve this problem...