I do not think these cards are there yet. The 4K input cards that are here now, use 4 PCI-E v2 lanes. So that would limit them to 2 inputs at 8 lanes for most motherboards.
So they need to utilize PCI-E v3 first to get more bandwidth. You can insert multiple cards into the same system though, keeping in mind how the lanes are divided between slots.
Keep in mind that when you run in 4K, your system will be at it's max 4 times faster than at 1080P, so if you would have 4 4K inputs, it will be the same as 16 inputs at 1080P when it comes to bandwidth. Even more because the output is also 4 times bigger.
I doubt it will scale up much further than that with current hardware.

That will be three 4-lane cards in total, or two 8-lane plus one 4-lane, depending on the 4K standard. Only problem is that the current high-end Intel X99 chipset has problems with vMix at the moment, making it harder to build a suitable system for it.