CM, suggest you provide more information as to HOW these boxes might be stacked.

So, e.g. in racking or as standalone and what configuration?

As example if you stack each straight on top of the next the pile will be much less stable than if built in a pattern - nobody should build brick walls with one brick directly on top of the one below!

You have only given two dimensions of the box, so harder to think of stability. The bottom box will have over a tonne on it so yes, you need to find out what the manufacturer of these boxes recommends as a safe loading when stacking. Are these boxes commercially available elsewhere or even on the supplier web site for info.

If they want to sell them then they need to provide info.

The missing dimension could have a huge impact on stack stability if it is less than 1m I would suggest not going over two high.

Other considerations are:

box fill - is the content tight against the walls or is there air space / packing around the contained goods

Content - whilst 350Kg may seem heavy is the content likely to be damaged by weight placed on top

Material - is it a sturdy solid board case, a heavy duty corrugated or light weight corrugate

Load point - some boxes derive their strength through the wall (all corners in alignment which you seem to be preferring) whilst other designs rely upon brick style  interlock to provide support

You are approaching this from the wrong direction however - if it is absolute these must be stacked four high then you need to design the packing to suit - a box may not be the answer but a packing case or wooden crate may be.

What are these boxes made of and will they be stacked indoors or outside exposed to the elements.

Is your facility Sprinkler protected, if so have you notified your insurer.  A fire occurring in the bottom layer may not be extinguished by high level sprinkler heads.