I did things a little different last year and got 6 hives pretty quick. I did wait till I had a full brood chamber just to make sure the first hive could recover quickly. Also, I have 3 med boxes for a brood chamber instead of deeps. That said, I took 5 frames of eggs/larva and put them in a nuc box and threw in some extra bees to help out (3 more frames). I let them go for a couple weeks and they made about 20 queen cells across the 5 frames. As soon as they capped the queen, I took each frame and put it into another box (5 boxes total) along with two more for each from the original hive, plus 2 more undrawn frames for them to work on. This made 5 nucs, which converted into 5 hives, plus the original.
I probably could have done it again after a month or so. And could have done it with each of the new hives when they reached full brood chamber.