all but splits on three broods
Three brood boxes? What size box? If deeps, that is about 150,000 cells? How prolific are your queens?
Lets have a quick think about this. Say one third of the frame area is nectar/honey arch. That leaves about 100,000 cels for queenie to lay up. Say cells are cycled every 25 days, so she is laying 4000 eggs every day? Amazing queens you have. Lets assume 6 week life span of a worker. Six weeks would see an over-160,000 bee population? About twice the size of a really large colony.
We once had one forum member who claimed her bees filled a box with brood in a week and then stopped laying for a few days. This is about on a par with that.
Even a sustained 2000 eggs per day only requires a single brood (just) so a brood and a half would suit her. Possibly better if the honey arch is the other side of a queen excluder, too, thus allowing more cells for brooding in the brood box.
I run 14 x 12 frames and rarely need more than a single brood - usually the queen is allowed into upper shallow(s) for a short time at peak lay rate. This leads me to believe that three broods on every hive is an unnecessary exaggeration.
Successful beekeeping can be achieved without extreme practices. It can do without unnecessary exaggeration, too.