Ideas to stack multiple PCBs on top of each other?
Board to board connectors are what you're looking for. SMT of course
In this answer I discussed using these spring connectors to connect boards:
Available in lengths up to 30 contacts, 1.27 mm or 2.54 mm pitch, so that a 10 contacts version doesn't have to be wider than 12.7 mm. Like I explained in the other answer this doesn't fix the boards mechanically though, and I explained in the other answer how I used snaps in the enclosure to fix them.
If you have a custom enclosure this is the most easy way of mounting: just push the different PCBs down the snaps. No screws, no mounting holes. The spacing between PCBs is 3.81 mm (0.15 inch).
If you have the space for these on every board, you could try using long male headers to stack multiple boards on the same pins:
https://www.sparkfun.com/products/10158
If you want to be able to seperate the boards again you can use feed through sockets on the top boards.
https://www.samtec.com/products/hle