I have no idea where the limits are for hardware/firmware/bios/software, but I would think it would be possible. If you dive low enough in the OS you should be able to have complete control over the messages going to each motherboard PCI-e slot, and if so you could negotiate whatever needs to be negotiated to multiplex over the 3 GPUs. Best case is if it just looks like a bridge and there already exists a driver for it, and then it might just work out of the box.
I discovered the XIO3130 from it being mentioned here
. This suggests
that it can work without hacking the host all that much, although when you stuff 8 in there things might start to change.
I've made electronic circuit boards before but only for microcontroller stuff with big fat traces that run at tens of MHz. No way I can do a BGA at 2.5GHz.
Where are the FPGA guys?