VGA capture cards

Hi all. I'm looking to build a PC to record from four VGA inputs, and I'm currently researching VGA capture cards. So far it's been pretty hard, there are very few models out there, and almost none of them encodes to h264 or anything similar.

Do you know of any PCIe VGA capture cards? Preferably supporting more than one input per card and integrating h264 encoding on-the-fly. Looks like Blackmagic doesn't offer any product that covers this use case.

Thanks in advance.