The most common and most likely answer to this crossword clue is the 1 plus 8 letter word A FORTIORI
I've seen this crossword clue in The Guardian
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More clues leading to the result A FORTIORI
- Moving to Fair Isle, fixing sort of gate with even more reason
- With more reason, one enters far too confused a state
- Citadel with excellent fencing or one with stronger premises
- If a riot erupts, soldiers must be brought in with more reason
- Defensive work by two protecting men on area with better grounds
- With a better argument, American Mancini ultimately pens ‘keep Moon River’
- Stronghold with excellent fencing or one with better grounds
- Possibly for a laugh, back independent or for a stronger reason
- Trunk road circling castle
- Excellent to beset castle I supplied with soldiers, having stronger reason
Buddy explains!

The straight part
We know that "With a better argument" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case with a better argument = a fortiori.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.