The thing about buying discount tickets and then adding on a day or some other upgrade at the parks is that you lose the benefit of the discounts. You will have to pay the full difference between gate price and what you paid up front. Current gate price for 6 adult and 1 child 4 day, 1 park a day tickets is $1805, so it would cost you $366 to add on a day once you are at the parks. Some people occasionally report having the good fortune of getting full price ticket value applied when upgrading discounted tickets and that's great if it happens, but it can't be counted on.
As far as when to upgrade, you can do so right up until park closing time on your last day of use, so you could wait until your third day in the parks to add that fourth day if you want.
Thanks for the clarification!