She has half a mind to double up! (4)
I believe the answer is:
mimi
'she' is the definition.
'half a mind to double up' is the wordplay.
'half a' suggests halving the letters.
'to double up' becomes 'mi' (I can't justify this - if you can you should believe this answer much more).
'mind' cut in half is 'mi'.
'mi'+'mi'='MIMI'
'has' is the link.
Can you help me to learn more?
(Other definitions for mimi that I've seen before include "Bohemian girl" , "Tragic heroine" , "Puccini's seamstress" , "unfortunate sewer" , "Tragic Parisienne" .)