What would a group of multiple floors be called?

[Ashtagon]

On the Wikipedia article for the Petronas Towers in Malaysia, these are referred to as "zones".

[Kriegspiel]

For subterranean dungeons specifically, I like the term "deep". e.g. the second floor of the third deep. It's sort of Tolkien-esque ("drums in the deep") which is nicely thematic. There's no reason why a deep couldn't also have a unique name or that named areas/zones or even levels could extend into or span across multiple deeps, in much the same way as dungeon levels or areas within those levels do. "Deep" used this way is simply a sort of collective term to designate literally how far down things are (in much the same way, as mentioned above, oceanographers and geologists might use the word "zone").

Awesome term. Oozes flavor.

[Psyren]

Sector, Tier, Division, Block, Wing...

[Asmotherion]

I'd call it a sector.

[KillianHawkeye]

"Zones" makes me think of the Sonic the Hedgehog games.

[Vahnavoi]

Video games just took common terms already in use elsewhere. Every term mentioned in this thread, has been used by some game.

[Theodoxus]

This isn't exactly what you're asking for, since this thread has pretty much proven that there isn't an existing answer. But I think if I had a 100 level megadungeon, and it was divided into 10 smaller macrodungeons, then each dungeon would be known as a Theme.

[Bohandas]

On the Wikipedia article for the Petronas Towers in Malaysia, these are referred to as "zones".

As an aside, has anybody else noticed that Petronas Towers matches the description of the Guide building from Restaurant At The End of the Universe