This may help, but only slightly.
The problem is that when you roll over uneven surfaces, its very likely the box will be supported by only 2 diagonal wheels. Boxes like Snap Ons have suspensions- springs on the casters compress to allow the opposite wheels take some load. But no matter what you do, your box is twisting. Over time, that can fatigue or permanently (plastically) yield your box. Pneumatic tires help a small amount.
A sheet of plywood or a 1/2" steel plate, while both a step in the right direction, won't stop the twisting. Angle iron as pictured above is better. But while angle iron is stiff in bending, the twisting I'm talking about is torsion (axial twisting) of the angle iron. And angle iron isn't good for twisting. An X frame instead of the rectangular picture frame would be better. As would thicker weaker material. For example- doug fir 4x4s might be just as stiff as 1-1/2 angle iron. (dunno, have to do the math).
A well made box is the best solution. Thickness of steel helps, but good welds, either lots of spot welds or continuous welds, really makes a big difference. And this is one of the things guys like about the truck boxes or Lista boxes.
My thinking is, the HF boxes are perfect for home shop guys who move their boxes infrequently. They offer plenty of storage and as ing as you can live with the drawer weight limits, you are good. But for pros on the move, they need a box designed to be rolled around. Where I work, they use Lista or SO KRL for this.
Another alternative is to use a roll cart, which many pro techs use. Their primary boxes are so big, they are just too heavy to move or there is no place else for them to be, so tools are transferred to roll carts and transported to the job. I think shade tree guys would benefit from this as well. Why not build your box into your work bench, or leave it on the back wall of the garage? Even if you only move your tool cart 10 feet, I think it's worth it.




If so, what do your co-workers use? Maybe emulate what is already a known solution in your work environment (assuming there are others who move their boxes).