getochkn :
Doesn't exist. The x99 chipset only has 40 lanes available, 4x16 would be 48. I think there are some configs that will let you do 4x8 though, which 8x should be enough in reality. Nothing tops out 16x yet really.
Of course it exists. Something like ASRock X99 WS-E LGA 2011-v3 provides support for 4 PCIE 3.0 slots at full 16x speed.
It uses a plx chip (2, actually) to multiplex 16 lanes into 32.
With that said, I'm not sure if it is really worth it as gaming cards don't saturate an 8x slot anyway; Puget systems published some benchmarks a while back with titans showing an actual in game difference of at most 0.6fps (within the margin for error) between 8x slots and 16x slots. But to each their own.