[woodnthings]

that's a weak design

The stacked shelves and dividers offer little structure and will have to rely entirely on the connection between them for resistance against racking. Also those planks are huge and will have some momentum if pushed and will want to keep moving.
The look is great, but you will need substantial brackets or angles to secure them. A back will help or diagonal rods or braces of some sort.
A rectangle will fold over easily, where a triangle is structural. Bridges are made with triangles in the trusses, not rectangles.

 

[woodnthings]

If you can ....

Make a drilling jig and drill 3/4" holes through the shelves and into the sides both top and bottom. Aligning the holes is the tricky part, but a drill jig will work. You can then insert dowels or pipes in the holes and start stacking them one on the other. The holes need only be 3 or 4" deep into the sides...a wild arse guess on my part, but keeping with the size of the stock which is "beefy" :yes:

No braces will show, as I think that is your intent? :blink: