Do you know what chipset the board has and the maximum you can set manually in the BIOS? If you can manually set above 2666, is the DRAM voltage adjustable?
2400 is the maximum stock speed for a 7700K and with OEM systems, that is often the max you're allowed. If you keep the existing stick, you'd be limited to 2400 anyway.
7th gen systems don't officially support 16Gbit memory, which could make it tricky to avoid high density memory. What stick do you have now, I assume it is dual rank?