Challening Overlapping Pattern and Trim

I have a process question dealing with lists and sequencing.

In the files attached, I have surface with a pattern.  The squares of the pattern have offsets that intersect each other leaving voids that are then cut from the main surface. The general organization is 3 objects in a group that interact arrayed on a grid on a divided surface.

What I would like to do, is to create an overlapping effect of each of the groups of three, that way when they get large enough to overlap (depending on distance from control points) it is not just a mess of lines, but one group gets priority and trims the out the object below (see attached overlapping02 image).

I setup a simplified attempt at getting this to work with a circle and grids, and although it "works"...sort of, it would be way to tedious to complete it on the more complex model or scale it up depending on the project.

Are there any thoughts on a good process?  Should I consider creating a script of some sort?  That may be above my level...

Thank you,