jen,
1. if you want extra bees, a full divide (maybe minimal honey and swarm management)
2. if you want honey, a light divide/nuc (honey and swarm management) you can do a very light spit/nuc on a booming hive that you want to make honey from, just take enough frames out, depending on the size of the colony, and how well the queen is laying and at least 2-3 frames. this gets you some swarm management, a honey making hive, and a new small colony of bees that will make honey next season.
3. you can super up without any divide whatsoever, i have. i have also added foundation with no queen excluder on until it is drawn. you take a chance on this (supering). just keep looking for swarm cells and make sure the queen has plenty of laying space. if one or the other starts to happen, you need to take away from that hive for swarm management.
hope this made sense?
EDIT AND ADD:
4. suggestion from jens post #11....EQUALIZATION of the hive.........
sorry jen, i sometimes forget all the options...........