We do it all the time at our local grocery. I will buy the limit in one transaction, DH will buy the limit in a second transaction, oldest child will buy the limit in a third transaction, and the youngest child will buy the limit in the fourth transaction. Since we typically shop together and with cash, this is not a big deal.
We also live within blocks of the grocery store so have been known to go back a day or two into the sale and pick up another round.
Usually we employ this strategy with items that can be frozen (cheese, frozen veggies, butter) that don’t go on sale super often at that price. We have done this for eggs as well with a limit and just purchase enough to get by for a month as long as we have the fridge space.