Consider bananas or apples or another offering (15)

I believe the answer is:

counterproposal

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'another offering' is the definition.
The definition suggests a singular noun which matches the answer.

'consider bananas or apples or' is the wordplay.
'consider' becomes 'count' (synonyms).
'bananas' is an anagram indicator (informal term for mad).
'or'+'apples'+'or'='orapplesor'
'orapplesor' with letters rearranged gives 'erproposal'.
'count'+'erproposal'='COUNTERPROPOSAL'

Can you help me to learn more?

(Another definition for counterproposal that I've seen is " Alternative".)

I've seen this clue in The Times and The Sunday Times.

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