Sounds to me like they need supers ...
FWIW, I've been experimenting with extra-deep frames, and one colony in particular is on eleven 14"x14" frames, which together provide the same comb area as the Modified Dadant which (afaik) is the largest volume of all the 'standard' hives.
'Successful' doesn't adequately describe the situation which now exists. Last week I struggled to do an inspection, and at first thought that the frames were stuck fast - but they weren't, they were just too bl##dy heavy to lift with only fingertips. Each frame has a good 3"-4" of capped honey at it's (thickened) top, with maybe half of the brood area lower down being back-filled with nectar. I can only guess at their weights - I'd say somewhere around 25lbs each at the moment, and getting heavier by the day. Clearly with such large volume hives there is a requirement to employ supers for honey storage.
From a survival perspective, this situation is brilliant of course - as such a colony clearly needs no assistance from me - but although hugely successful in that regard, it doesn't fit easily into the life of this apiary which is directed towards nuc and queen production, and not honey. And so - very reluctantly - I'll be terminating the experiment at the end of this season, and reverting to the use of larger numbers of slightly smaller (14"x12") combs, in Long Hives housing 17-20 frames.
LJ