Well, Western Mediterranean =/= Sicily and Magna Graecia. I don't think any of the Greeks to be interested in annexing Iberia and Gaul...
During the Third Sicilian War, Agathocles invaded the Carthaginian mainland with 14,000 men. Now, I doubt he could have forged an empire, but if a more powerful Syracuse (let's say it has all of Magna Graecia), or really any Greek state more powerful than Syracuse was at the time of Agathocles, did the same thing, and succeeded, then they could have taken territory from Carthage, maybe made an independent Greek state like was done to Cyrenaica and the Ptolemaic dynasty (though that was more like a revolt--this mostly-Punic/Numidian/Lybian state would be appointed with a Greek ruler perhaps, and then settled with Greeks from one or more mainland Greek city-states). Syracuse in this case would be quite happy to take Sardinia and Corsica along with Sicily. If a state, that had established this 'Mediterranean empire with only part of the Mediterranean' like we've said, that had the Magna Graecian cities as its puppets, occupied parts of the Carthaginian Republic, they'd be plenty happy to annex other parts as well.
But it's still absolutely no way for them to established a total sovereignty over the Eastern states/kingdoms...
If another state doesn't establish a huge empire on the other side of the Mediterranean, then they easily
can. Hell, they could even if one did--look at what powerful Rome did to the absolute monster Carthage in the First Punic War.
Not really...especially if the status quo could be achieved and maintained betweeen those cohegemons.
One of the cohegemons could easily go to war with another for some tiny little reason like the Roman Republic did with Carthage.