Swarm control/very busy hive

[Richardb]

I’ve got three hives two of which are incredibly busy. I’ve added an extra super 2 weeks ago which they have pretty well already filled. I could add another super but the brood box is absolutely full with very little space for the Queen to lay mainly with brood in all stages. There are no queen cells but someone has advised me to do a Pagden swarm and so long as there are eggs and early-stage brewed the colony without the Queen will just raise a new one.
Does this sound sensible and what would the more experienced beekeepers recommend?

 

[masterBK]

Hive in right state for carrying out a Demaree which can combine swarm prevention with producing a few queen cells in the top box if done properly. Not sure I would recommend what has been proposed to you (a walk away split?). Keep the strength in same place if you want honey.

 

[enrico]

Not sure why you aren't thinking about adding a another brood box!
E

 

[Eyeman]

Sound like you queen needs double rather than single brood. Also keep those empty supers going on.