Have more sense than to become further acquainted with (4,6)

I believe the answer is:

know better

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'to become further acquainted with' is the definition.
I know nothing about this answer so I cannot tell whether this works.

'have more sense' is the wordplay.
'have' becomes 'know' (synonyms).
'more sense' becomes 'better' (I can't explain this - if you can you should believe this answer much more).
'know'+'better'='KNOW BETTER'

'than' is the link.

Can you help me to learn more?

(Another definition for know better that I've seen is " Be wiser".)

I've seen this clue in the Evening Standard.

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