IMO there's more to it than just adding a box, plus,
it depends on what your goals are.
The average backyard beekeeper may not have honey production as a priority.
The books note that some people leave beekeeping because they can't
figure out what to do with the surplus honey.
In that case, the goal is setting back the swarming triggers of swarming.
That means either splitting to knock back colony strength, or
manipulations that give the queen plenty of space to lay eggs in,
and to give the bees a space signal by putting in frames that need to be
drawn out.
• When 80% of the gaps in the hive are pretty full of bees, the hive
needs more space, WHETHER OR NOT THE HONEY SUPER HAS ANY HONEY IN IT.
Add a box. How you do it is important. It depends on your strategy,
your style, your goals.
• When the nectar flow is strong (and it is now) you need to go through
the frames in the brood box(es).
Frames of honey need to be moved up into honey supers.
Frames of mostly (all) pollen need to be moved up or out. If full of
capped honey, harvest. If no honey, pull and renew. If with brood and or
honey, move into the super until you can harvest it.
Replace those frames with drawn brood-size comb.
Depending on the strength of the colony, maybe an undrawn frame next to
or in the brood ball.
(Easiest with foundationless frames because there's minimum risk of
catastrophe, and bees love to build comb in open space, compared with
either wax or plastic. )
These adjustments usually force the addition of another box to the colony.
• Harvest capped honey frames, or move them to the top of the hive to
the slots nearest the box walls. On the hive is the safest place to
store honey.
DON'T just put pulled honey frames into a bin. Wax moth love a closed
space like that. So do small hive beetle. If you need to store them in
a bin, freeze in the freezer for two days first.
I've noticed this year that colonies don't want to extend the brood ball
into deep frames below a medium box full of brood frames. They use
medium frames close to the brood ball.
Haven't they been reading the books?
When you have 7 or 8 brood frames in the bottom box, and want to get the
colony to expand into the adjacent box,
move three frames to the next box, and flank those frames with drawn
frames of brood comb.
The thing is, they may start filling those frames with nectar and honey
too. Gotta move them up into the honey supers.
ps
A box full of honey frames is a queen excluder. Less resistance to the
honey work-force than a metal grate.
that's my 2¢