Is there a workaround for destroying multiple objects at different times?

Sure, why not, I’m using sphere here to pick up herbs. You can use another collision volume to chop trees.

But one is usually enough, why complicate things. Check what you overlap and then decide what to do with it. You may have your reasons to use many overlapping components, of course - a robot with 3 different arms may pick up things in 3 different ways, for example.