The concept is still going to be about the same, in that you'll need to check where the touches are occuring and take appropriate action if you're going to overlap like your reference seems to, you'll also probably want to manage which objects can be hit, which may be best done by treating them differently if another instance is on top of them. I'm trying to look in to how you could fix that, and the best I've found is that you probably need to be utilizing device input instead of standard mouse inputs.
Looks like a weird EBA / Osu! sort of thing, but I getcha.