She has many a song in West Side Story (5)

I believe the answer is:

maria

I'm a little stuck... Click here to teach me about this clue!

Here is my best explanation:

'she' is the definition.

'many a song in west side story' is the wordplay.
'many' becomes 'm'.
'a song in west side story' becomes 'aria' (I can't justify this - if you can you should give a lot more credence to this answer).
'm'+'aria'='MARIA'

'has' is the link.

Can you help me to learn more?