You cant off the shelf. Im the one that designed this system with Padrino. My personal prototype systems are running 10 GPUs of a Gigabyte board. It requires very low level changes to how the board BIOS operates.
How have you started 10 GPUs? My personal record is 8 at the moment. And I want to start 12. What OS?
You can run 32 cards from one Motherboard using Linux Zcash miner under Ubuntu and a combination or risers and PCIE-X3 splitters. Not sure why you would want to, but you can.
Even with pcie switches how are you compiling the kernel for 8+ gpus? Much less bypassing current mobo restrictions to get over 16 gpus?
There are multiple things in play to have systems support large numbers of any PCIe card, GPUs of various types require different addressing so the specifics depend on what you are doing but in short it's a combination of the motherboard itself, the OS' ability to handle the cards/addressing, the driver (fglrx or amdgpu), Xorg, and the application using the GPUs. Currently I have 16 GPU systems as my maximum in development, the 8 GPU system has been on the market for a few months now.