Comment by michaelt

The card in the bottom slot can overhang the board, if you only need to add a single multi-slot card.

Beyond that point you're probably looking at getting a server. Boards like the X9DRG-OF have eight dual-width slots, and you can get them in a quadruple-power-supply configuration - which you'll want when you add up the power consumption of a bunch of GPUs. Anything rack-mount will be very noisy though.

Another options is a cryptocurrency mining style 'open frame' system with PCIe risers. Google that and you'll find some crazy setups enthusiasts have posted to reddit.

Or you can just run something in the cloud - you can buy a lot of cloud time for $6000.