If I end up with more than I can carry in the single pannier, I attach it to the rack with a couple of bungee cords that I always carry.
+1, but I take a bunch of clothes out of the bag/pannier to make space for groceries. Clothes go in a plastic bag (I usually carry one just in case, or buy one with groceries) and that gets bungeed on top of rear rack. Securing groceries with bungee cords can be tricky, clothes are easy in that regard.
--J