Crazy outfit with nearly every single song (8)

I believe the answer is:

madrigal

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'single song' is the definition.
'madrigal' can be an answer for 'song' (madrigal is a kind of song). I am not sure about the 'single' bit.

'crazy outfit with nearly every' is the wordplay.
'crazy' becomes 'mad' (synonyms).
'outfit' becomes 'rig' (rigging is a kind of outfiting).
'with' means one lot of letters go next to another.
'nearly' means to remove the last letter.
'every' becomes 'all' (similar in meaning).
'all' with its final letter removed is 'al'.
'mad'+'rig'+'al'='MADRIGAL'

Can you help me to learn more?

(Other definitions for madrigal that I've seen before include "Elaborate part song" , "Unaccompanied harmonised part song" , "Old part song" , "Unaccompanied song in several parts" , "Part-song" .)

I've seen this clue in The Telegraph.

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