The only captue card i know that will handle 3-4 1080p inputs is the
BlackMagic Decklink Quad Studio for £625, which will require you convert all DVI/HDMI signals to HD-SDI to be plugged into the capture card.
So to do this with a capture card you would require...
1x BlackMagic Decklink Quad Studio ~£625
3x DVI/HDMI spliters.
3x
DVI/HDMI to HD-SDI convertors ~£185 each.
Then some software to capture the multiple inputs simultaneously and of cause a powerful rig to capture all this in real time to a disk or rather array of disks/ssd.
This of cause is the most ideal solution but also the most expensive.
A cheaper alternative is to use the likes of DXTory to convert/capture the DirectX feed into a WDM webcam style feed that xsplit could then use as a capture device, with xsplit setup with a custom resolution to then record to file.
Note that if you are looking to upload to you tube then you need to keep the maximum width of the recorded output no more than 4096 pixels wide.