We had the same thought - maybe not a stack a mile high but at least enough for a few RPis and daughter boards etc.
We came up with the thing you can see on http://www.thepishop.org/cases.htm
and it is infinitely expandable.
The top and base are held together with 25mm spacers through which go 3mm bolts.
The next step is to use 3mm studding and lock nuts so a PiStack can be as deep as you like.
We've put the dimensions on the web site so you can make things to fit (or even make your own.)
We will have production within a couple of weeks (given a following wind!) and we certainly welcome suggestions about how the PiStack idea could move forward.
We have our own on-going project which would see an RPi at the top of the stack and some sexy daughter boards underneath controlling the rest of the planet <g>.
Life's single regret: not patenting dongles when we invented and named them to protect the Wordcraft word processor on the Commodore PET!
You can buy 31 RPi3s for the £639 price of one Samsung Galaxy S7 Edge smart phone - who buys this stuff?