Cats maybe fight Melody Maker in case (7,3)

I believe the answer is:

musical box

'melody maker in case' is the definition.
(music-making device in a box)

'cats maybe fight' is the wordplay.
'cats maybe' becomes 'musical' (Cats is an Andrew Lloyd Webber musical).
'fight' becomes 'box' (boxing is a kind of fighting).
'musical'+'box'='MUSICAL-BOX'

(Other definitions for musical box that I've seen before include "It plays a tune when opened" , "Tune-playing casket" , "Tuneful container" , "Tune player" , "Wind-up tune producer" .)

I've seen this clue in The Times.

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