Birger,I was faced with the same issue when I made a version of an old post office (US post office) for my wife’s wool materials she uses in her weaving.

I wanted to have some symmetry for the various cubby holes but wanted the divides to be relatively thin (main vertical dividers are 15mm and horizontal dividers are 9.5 mm). I worried about the strength of the joints (like you) when two horizontal dividers were attached to the same vertical dividers, at the same location. I wanted to dado the corresponding horizontal dividers into the vertical dividers. Just doing a dado would make the vertical divider too narrow at the point of the joint. Therefore, in addition to the two opposition dados, I made narrow mortise and tenon joints (about 6 1/2mm square) extending from one side to the other. Also, rather than have the tenons meet at the same location in the vertical, I staggered one pair with another. This offset preserved the integrity of the opposing dados on the vertical pieces.
I try to illustrate my discussion with several photographs.
Photo 1 shows the completed project.
Photo 2 shows it filled with the wife’s wool materials
Photo 3 shows a pair of tenons on a horizontal divider. I can not show how the tenons are staggered between the opposing horizontal dividers.
Photo 4 shows a pair of opposing dividers in the respective dados.
If my description is not clear, please contact me and I will sketch up a drawing.
Harold Blair