There are systems like this, but not some we see in here as they are often for commercial use, i actually ran one such system years back but it was only 4 SD channels and the cameras was regular analog CCTV models, so no HD back then.
You have to be careful when looking for these, they can be lesser resolution then 1080p, also the bitrates they use can be lower than you like, FPS can also like some CCTV systems be less than 24 / 30 FPS.
I got my system from ebay back then, also where i have seen others of these 4 channel systems.
Mind you the cameras they come with, geared for larger commercial vehicles, so for instance the side cameras, well probably not kile tesla side cameras but more on mirror tree mounting
You should maybe search with " 4 channel vehicle CCTV " rather than 4 channel dashcam.