WI : Republic of Amalfi remains under Roman control

As title really, in the early days of the republic it was under Roman control and started to dominate trade in North Africa and beyond.

I'm curious as to what the impact would be if the Republic of Amalfi stayed under Roman control, but was able to flourish and expand its trade ties within the Empire and beyond.

What impact could this have on the Romans culturally?
If it seeded sister republics within the Empire, could they outshine them?
What would this do for Roman fortunes in the Med?
What could this do for the Romans in Italy and the Western Med?
 
I had to look this up as it rang no bells - now I see, EASTERN ROMAN control!

I find it hard to unravel its history from what I can see - the Normans especially seem to be a problem here
 
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