Not possible with textures, either technically or physically. (including bumps/normals)
Possible with models though, however it'd mean having to have specific ones made & in the shop, plus would involve either having collision detection that clips through them or make the game lopsided & kill the balance by having full collision detection (which would also make it run slower for a lot of people).
Not to mention that current textures wouldn't map to the different objects so each one would have to have a specific texture item. Not too sure how people would feel about that.