I downloaded an app that is supposed to do this basically.. you scan bar codes while shopping.. if it's cheaper elsewhere in your town it will tell you. If it's not in the database, you can enter it. You get some sort of reward points for entering new items. Unfortunately, even basic items I scanned were not shown for my area, so I haven't bothered with it too much.. I mean time is money too right.
It's called price spotting.
Have 4 people to shop at the same time would be great, if you had 4 people who would want to do that. You would also have to all drive and meet up and swap groceries out of one bag and in to other bags and probably there would be someone mad because you bought chicken thighs but they wanted chicken breasts.
Also probably after a few times it would become apparent who had the best prices for what, similar to keeping a price book.
I also downloaded 'out of milk' which is a pretty good grocery list app. I'm not sure how good it will be for comparing prices, but I'm trying to enter prices for everything for our primary grocer store to compare later.