SHORT VERSION: When adding another hive body (or super) to a hive because the population is expanding and crowding all the frames, I try to pull up two or three frames of brood to reduce the chances of the queen becoming honey bound. I also surround each brood frame in the original hive body with blank or drawn comb to encourage the queen to fill them with brood. All of which may or may not reduce the chances of swarming.
LONG VERSION: Whenever I add another hive box (or deep) to a nuc or colony that’s population is expanding, I pull up two or three frames of brood while I’m at it because, on her own, the queen won’t always expand the brood nest up into a new deep. The worker bees fill it with honey instead and the queen becomes honey bound (or trapped in by honey with nowhere to lay), which can trigger a swarm, not something most beekeepers want.
Some people call the pulling up of brood pyramiding or creating an unlimited brood nest. It’s also similar to checker boarding. But it all seems like a variation on a theme to me. Pulling up brood encourages the queen to expand the brood nest up (not just to the sides), thus reducing the chances of her becoming honey bound.
So let’s say your deep has six frames of brood. You pull three frames of brood from the middle and then put a new frame (drawn comb, foundation or foundationless frame) between each remaining frame of brood, thus providing space for the queen to lay between the frames of brood. (The bees will have to build comb first if the new frames aren’t drawn comb, but that’s not bad because it gives the bees something else to do — fill in space with new comb — instead of preparing to swarm.) Then you add another deep and put the three pulled frames of brood in the middle, with empty frames on the sides. This new configuration of brood is in the shape of a pyramid and now the queen has plenty of room to lay in the lower and upper deeps (or hive bodies).