Gotta disagree with the whole no water in the cooler thing.
Dry cooler, what’s keeping the goodies cold? Direct contact with the ice and cold air.
Wet cooler, what’s keeping the goodies cold? Direct contact with the ice and cold water.
Simple question, would you rather spend the next two hours in a room with 35° air or a pool of water at 35°?
(Just checked it, glass of 70° tap water, handful of ice cubes, five minutes later with an accurate instant read thermometer ~35°.)
One leaves ya cold, the other leaves ya dead.
The other thing is all that water increases the mass that your trying to keep cold. A big pitcher of ice water stays cold a lot longer than a glass of ice water does.
The biggest cooler (with the thickest walls and an insulated lid) you can find/justify for the amount of stuff you plan to keep cold, plus room for the ice! One big cooler is better than many smaller coolers.
Block ice and cubes; blocks for a long slow melt, cubes to fill the gaps between the stuff in the cooler.
Keep adding ice as needed (removing excess water as needed), but never let the amount of ice (block or cube) get too low. It’s easier to keep a cold cooler cold, once it starts to get warm your back to square one and you’ll need more ice to get back to where you started than you would to keep the temperature steady.
Never put anything that isn’t already cold, or preferably frozen if it can be, into the cooler if you can avoid it (e.g. the steaks for the first nights dinner cold, the burgers for night two frozen. Excess melt water from the cooler, or as Harmonious Discord suggested any cool water can knock 10° or 20°+ off that sixer before you put it in the cooler to get cold.).
If your not near an easy source of ice an extra “ice only” cooler ain’t a bad idea (Preferably one that fits into the big one. You can shift the really perishable goodies into it and put it in the big cooler with the drinks when the ice starts running low).
Keep the cooler out of the sun, or anywhere else that’s warmer that the ambient temperature (anybody who’s spent a late night by the campfire knows how pleasantly oven-like a tent is at 11:00 AM). Cover it with heavy, soaking wet cloth (thick blankets are much better than towels), basically a swamp cooler for your cooler.
Big caveat, when I was worrying about keeping a cooler cold it was filled with highly perishable comestibles, not just tasty beverages. So for me it was a choice between a week of shits and giggles or a week of shits and projectile vomiting!