Frankly, the moment that Ptolemaic Egypt accepts that it is Greek and Egyptian by this point (i.e. creates that syncretic culture and joint gods, etc) then I think it is the best option for dominating the Mediterranean. If the Romans hadn't come along, I fully expect Ptolemaic Egypt finally conquers Syria and becomes the hegemon of the Greek-speaking world, and be able to reunite it.
At which point, with the exception of the possible Samnite/Etruscans in Italy, the Ptolemaic Kingdom can just bring the Greeks into their sphere piece by piece. With control over Antioch and Alexandria, they can station a number of forces in Antioch, and when times are quiet, bring the Anatolian coast into play, from which later on Alexandria can continue to fund expansion.
I'll assume that they'll adapt their administration (otherwise it could be any of their successors that unites the Med), but I don't see it implausible for the Med to be dominated via Alexandria, Antioch, Byzantion/Chalcedon, Syracuse, Tarentum (and maybe Athens).
As to Carthage? Without a major change to their character (not impossible, if you have an alt-Barcid dynasty) to change them from Merchant Republic to something more militant - I think they'd be eclipsed by the Ptolemaic Kingdom as they'd be dependent on the Kingdom economically as a customer, and the Ptolemaic Kingdom WILL be sponsoring further colonisation in the western Mediterranean (and 'inviting' existing colonies into the Kingdom), leading to the Ptolemaic Kingdom and Carthage actually butting heads, making invasion of Carthage worthwhile.
At which point, with the exception of the possible Samnite/Etruscans in Italy, the Ptolemaic Kingdom can just bring the Greeks into their sphere piece by piece. With control over Antioch and Alexandria, they can station a number of forces in Antioch, and when times are quiet, bring the Anatolian coast into play, from which later on Alexandria can continue to fund expansion.
I'll assume that they'll adapt their administration (otherwise it could be any of their successors that unites the Med), but I don't see it implausible for the Med to be dominated via Alexandria, Antioch, Byzantion/Chalcedon, Syracuse, Tarentum (and maybe Athens).
As to Carthage? Without a major change to their character (not impossible, if you have an alt-Barcid dynasty) to change them from Merchant Republic to something more militant - I think they'd be eclipsed by the Ptolemaic Kingdom as they'd be dependent on the Kingdom economically as a customer, and the Ptolemaic Kingdom WILL be sponsoring further colonisation in the western Mediterranean (and 'inviting' existing colonies into the Kingdom), leading to the Ptolemaic Kingdom and Carthage actually butting heads, making invasion of Carthage worthwhile.