Put too many people in cover - word spreads (9)

I believe the answer is:

overcrowd

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'put too many people in cover word spreads' is the definition.
I can't tell whether this defines the answer.

'cover word spreads' is the wordplay.
'spreads' is an anagram indicator (I've seen 'spreading of' mean this).
'cover'+'word'='coverword'
'coverword' anagrammed gives 'OVERCROWD'.

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(Other definitions for overcrowd that I've seen before include "Fill area to excess" , "Pack too much" , "Accommodate too many" .)

I've seen this clue in The Daily Express.

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