ᐅ Assembling Ikea Expedit 4x4 and 4x2 units into a 4x6 configuration

First of all, hello to everyone here in the forum.
I found this forum through a Google search, and as a big IKEA fan myself, I thought you might be able to help with my considerations/problem. 🙂

I have an IKEA Expedit 4x4 with a desk attached, with the long shelves positioned horizontally, and I want to place an IKEA 2x4 on top to effectively create a 4x6 IKEA Expedit.
I want to have as few thick outer frame parts as possible, definitely not two stacked on top of each other, as that would significantly affect the appearance.

Here is what I have in mind so far:
Remove the top outer frame of the 4x4, and place the complete 4x2 on top. Then either bond them together with Sikaflex (polyurethane adhesive) (removability?) or attach them with dowels into the two outer intermediate shelves. For the second option, I would have to drill holes into one of the end panels of the 4x2. Does it hold well, or is it too soft or hollow inside?

This way, I would only have one thick outer frame piece in between, and both units would be firmly connected.
PU adhesive should also be removable from a smooth surface if necessary (right?), after carefully separating the parts with a scalpel, and it provides a very strong bond.

By the way, for the 4x2 unit, I plan to remove the shelves from the middle four compartments because the printer will go there. I don’t expect any problems since nothing will be placed on top of that area.

Is there anything wrong with my plan? Or is there another way to leave out all the outer frames in between that I haven’t thought of?
I’m grateful for any suggestions! 🙂

4x4 .. 4x2 .. 4x6 .... ?????
Is this a math problem? 😉