Barracks at York

[Gaius Julius Caesar]

Or perhaps the stone barracks had more than one floor...allowing bigger accomodation and troops to be accomodated?

Indeed why not? Seeing that civilian buildings could be even higher, why not theorise about barracks being multi-floored as well? It could play havock of course with the current estimates of troops housed in such forts...

I guess it's up to archaeologists to look at the foundations for such estimates?

Possibly the upper levels were timber? Cavlary units wee known to keep horses in the barracks
in some forts I recall. The troops them selves could be in the upper?
Equipment stored in the lower levels, the troops again sleeping in the upper.