The most common and most likely answer to this crossword clue is the 6 letter word WORLDS
I've seen this crossword clue in The Guardian
W
O
R
L
D
S
More clues leading to the result WORLDS
Buddy explains!

The straight part
We know that "classes" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case classes = worlds.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does WORLDS mean?
WORLDS noun- (with "the") Human collective existence; existence in general.
- The Universe.
- (with "the") The Earth.
- A planet, especially one which is inhabited or inhabitable.
- A very large extent of country.
- (speculation) A realm, such as planet, containing one or multiple societies of beings, especially intelligent ones.
- An individual or group perspective or social setting.
- The part of an operating system distributed with the kernel, consisting of the shell and other programs.
- A subdivision of a game, consisting of a series of stages or levels that usually share a similar environment or theme.
- The twenty-second trump or major arcana card of the tarot.
- A great amount.
- Age, era
- To consider or cause to be considered from a global perspective; to consider as a global whole, rather than making or focussing on national or other distinctions; compare globalise.
- To make real; to make worldly.
- To a great extent; much; far