I thought and tried the same.. turns out no. Although in theory, the OEM could provide you a very custom BIOS to make it work, but probably at the expense of disabling other stuff on the board. I wouldn't ask let alone hold your breath. Basically the issue is that the PCI lanes are crowded with other "stuff", devices, SATA, USB, etc and there is just no more room. Here's an email I got from tech support at Asus about my Sabertooth Z170 S mobo (which I managed to only get 3 GPUs with):
We are writing back to you regarding the issue with your motherboard.
I checked and found that the system has not enough resources because 6th generation processor and chipset has only 16 PCI lanes access or 32GB/s.
_If you are using 6 graphics card on these specifications: _
2 x PCIe 3.0/2.0 x16 (x16 or dual x8) = 16GB/s or dual 8GB/s + 8GB/s
1 x PCIe 3.0/2.0 x16 (max at x4 mode) *1 = 4GB/s
3 x PCIe 3.0/2.0 x1 = 1GB/s
You can only use function 3 graphics card because of that. Furthermore, the system needs bandwidth on SATA ports and USB, so it will also share with 32GB/s or 16 lanes.