Little home of the house mice (4)

I believe the answer is:

semi

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'little home' is the definition.
'semi' can be an answer for 'home' (short for semi-detached). I'm not certain of the 'little' bit.

'of the house mice' is the wordplay.
'of' indicates a hidden word.
'SEMI' is hidden within 'the house mice'.

Can you help me to learn more?

(Other definitions for semi that I've seen before include "Co-joined house" , "House attached to one other" , "Common type of house" , "House; match" , "home perhaps" .)

I've seen this clue in the Evening Standard.

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