Up to three!
Today I installed a second nuc from Mary Bouma. This one has a new queen from this year. I installed this one into the white Long Hive, which is double-walled. So now I have both Long Hives occupied and one of the vertical hives. The plan now is to take a frame of brood from each of the first two hives, put a purchased queen with them and get the fourth hive going in a week or so.