This is very rare.
The only boards I've owned that do this, was the X99 ASrock Extreme 11, and the Z270 Supercarrier which had a PLX chip.
Why are you needing 3x full electrical 16x PCIE sockets? (Just curious)
You can do that on pretty much any HEDT board from X79 onwards natively. Your best option might actually be a Chinese X79 board. The Jingsha X79 P3 is generally considered to be a good one and is available for £75-ish. Pair it with a Xeon E5-1650 v2 (£50-60 on Ebay) and you should be good to go. It's more difficult on the mainstream platforms due to the inherent lack of lanes available, so you'd need a board with a PLX chip. Those used to be more common 5+ years ago on higher end boards. Something like the Asus P8Z77-V Deluxe will do x16/x16 if you can find one cheap on the used market.Okay what about 2 slots both being being a full 16x each.