I know of no company which makes such a system however not really hard to do save for one thing.. The stupid connectors are custom and each Back Up /Side Camera company used non-standard propertority connectors so you gonna have to cut and splice a bit.
Now, any DVR can do it provided you have an inverter.. I use a pair of REPLAY TV units that are .. highly vintage (Replay went out of business over a decade ago) but still work.. Though it is NOT working today. (it may be tomorrow) due to a broken wire one record option on the DVR's is a 'nose cam" (dash cam analog).
You can take a high end laptop add a WIN-TV card or two and splice into the leads from the assorted cameras to get base band video for the card to record.
A Stunt box (Video switch or video auto switch) may be needed.. You need about a gig of HD per hour more or less depending on the number of cameras and the quality.