I generally drop all four on the first area I hunt out west, just to burn off their energy. In the open prairie, it's not that chaotic, but can be. Generally run two at a time though. This past trip to Nebraska I ran all three frequently, rotating breaks as needed. In the grouse woods only run one at a time.
Pros - I think more noses on the ground more birds contact. Not all dogs scent equally and I have kids that show a dog on point downwind of bird and two running mere feet away unwind and never scent. I also think it can help cut off or pin running birds as one is tracking an the others are casting back from further out. Helps with cripple recovery too. The joy of seeing pointing and multiple dogs backing. Like running young inexperienced dogs with vets to build their confidence.
Cons - Expense of buying system that can handle 3 or 4 dogs. Chaos if dogs are not listening or just keeping track of them when running silent, GPS collars help that. Can lead to bumping birds. When dogs are birdie which one to follow, have had the issue of multiple dogs on point, I go to least steadiest first, then to next if they are still on point.
Just my two cents.