This is not really a strength issue but rather a flex issue.
I'm not sure if I understand your proposed configuration exactly, but I'm still working on my morning coffee. LOL.
Regardless, your biggest issue is the weight of the upper rack flexing the upper shelf of the lower rack and possible causing the boxes to sieze. I'm sure this is what you mean by strength.
If you can use some sort of shim or spacer than distributes the weight to the sides of the lower rack rather than the top shelf you will be fine.
It might also be worth adding a solid back to the lower rack, if possible, and seeing if you can configure it so that it takes some of the weight of the upper rack.
I've stacked many a rack, or used racks to hold other cages, but I always make sure the sides are taking the weight.