Classes take in the greatest common principles (9)

I believe the answer is:

generalia

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'common principles' is the definition.
I know nothing about this answer so I can't tell whether this works.

'classes take in the greatest' is the wordplay.
'classes' becomes 'genera' (more than one genus - a class or category).
'take in' means one lot of letters goes inside another.
'the greatest' becomes 'Ali' (Muhammad Ali, known as the Greatest).
'genera' placed around 'ali' is 'GENERALIA'.

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I've seen this clue in the Sydney Morning Herald.

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