So there have been a couple times where I've liked some part of an item but not all of it. I'm sure we've all time we've used a wall or a floor to modify how an item is shown.
How about selling invisible items that would hide whatever part of other items enter their area is hidden. You could sell various shapes and sizes.
... and it just occurred to me what a technical nightmare it might be to decide what texture is used on the cut bit.
Maybe the hiding item determines it? For example, you could have a large sphere that has a shiny golden texture used to close the cut bits.
I dunno, maybe someone can make something useful from this idea.