"In The Naked Time Uhura reports that Sulu is running around in "level 2 corridor 3". If this "level 2" is "Engineering Level 2" (otherwise wouldn't she say "Deck 2") then there are a LOT of corridors crammed into the top of the pylon - impossibly so"
If "level 2" would refer to "Deck 2" there also would have been a lot of corridors just below the bridge.
The "level 2" reference neither fits "deck 2" or alphabetic prefix nomenclature and made me thinking, too.
What deck is the outer area of the saucer that is on the same deck level
as deck 7 but has essentially no connection to the core of deck 7?
Because of the underside curvature of the saucer hull this outer ship's area can only be accessed via deck 6 and would rather seem to be the lower level of deck 6 or "level 2" than a part of deck 7 (and no need for Uhura to get into details if everybody aboard the ship understands what "level 2" refers to).
I can imagine Sulu having a great time driving the other crew members there in front of his rapier - they don't have that much evasion possibilities and space.