Checking for intersect, not including edge

[lclankyo]

Suppose I have 2 boxes where box1 sits on top of box2.

 

I'm doing:
box1.intersectsMesh(box2), which returns true because touch at the very edge. However, I only want to check cases where they intersect without including edge scenarios. I was trying to read through the documentations, but couldn't find anything. I did see a function called "intersectsPoint", but that can make my code messy because I would have to check many points. Is a better way? I don't want to make the boxes smaller.

Thanks for your help.