There are some commercial software options for this. On the Mac, there is Softron MovieRecorder which can record up to 16 video channels:
https://softron.tv/products/movierecorderOn Windows, VMix has a Multicorder option which can record up to 4 channels on its Pro and 4K editions:
https://www.vmix.com/help17/index.htm?MultiCorder.htmlAnd Metus Ingest also supports multi-channel recording (up to 16 channels depending on the recording codec used):
https://www.metus.com/metus-ingest/One issue to keep in mind, is that depending on the computer hardware and recording codec used, it is pretty easy to overwhelm the system when attempting multi-channel recording, in which case it wouldn't be able to keep pace with the incoming video and would start to drop frames.
I'd imagine four HD streams is probably doable on some systems, but four 4K streams gets trickier, especially 4K at higher frame rates (50 or 60 fps).