AHC : Amalfi - The Emperors Republic

Whilst the title is more for flair, I was wondering what feasibly could be done to bring Amalfi to dominate S.Italy after 839. Particularly dominate S.Italy, whilst being at least nominally part of the Empire.

Ideally I'd love to see the Prefect of Amalfi be the regular Katepan of S.Italy, but that is more bonus points.

(I apologise for the lack of details, I'm very short on them myself!)
 
It would have to rise to its prominence before 1343, when the earthquake/tsunami destroyed the city and crippled it for good OTL. A stronger city can recover from that, but it might have to be one of the premier cities of Italy to be able to rebuild back to its former glory.
 
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