Many Britons so classified graduate with me (4)

I believe the answer is:

bame

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'many britons so classified' is the definition.
I don't know anything about this answer so I cannot judge whether it can be defined by this definition.

'graduate with me' is the wordplay.
'graduate' becomes 'ba' (someone with a Bachelor of Arts degree).
'with' says to put letters next to each other.
'ba'+'me'='BAME'

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I've seen this clue in The Guardian.

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