WI: Greeks more successful in Western Mediterranean

I'm thinking about early Carthage-screw and stronger Greek presence in western part of Mediterranean Sea-what is needed to make Greeks more successful there?
Perhaps Phocaean full victory over Carthage and Etruscans resulting in Sardinia and Corsica being colonized by Greeks. Is it possible? If in addition Carthaginians are pushed out of Sicily Greeks should dominate European coast of Western Mediterranean totally, with Carthaginians reduced to their African core. How would it affect Greek (and Mediterranean in general) world? Would Greeks move even further west, having Gibraltar Strait open for their trade? Greek colonies on Atlantic coast, anyone?
Also, would wanked Western Greeks be able to crush Carthage completly one day, even in Africa? IOTL Sicilian-Greek forces of Agathocles invaded North African Carthaginian territory and with help of Greeks from Cyrenaica (and local Berber rebels, unhappy about Carthaginian rule) Agathocles hoped to conquer it. That would change Mediterranean Sea into Greek Mare Nostrum.
 
One thing that occurs to me is that colonists go to the best places to colonise - hence Sicily, the entirety of Southern Italy etc. But even though they maintained links to their origin cities (and leagues and whatnots) they all still fell in the end to Rome.

I realise that Marseilles was a Greek city, and I think there were some further West, but the main thing that occurs to me is that settling in any great numbers was not... ready at that time. S Italy and Sicily were still taking in people, still growing, and still of course challenged by Carthaginian, native (Sicilian or Italian, as applies), and Roman states.

IMHO you would need to have a situation where Magna Graecia retains its Greekness, and then Greek colonists etc would be more inclined to begin to colonise to the West, but over a couple of additional centuries.
 
Full control of Sicily would be absolutely essential to begin to expand Greek influence further into the Western Mediterranean and to simultaneously blunt Carthaginian ambitions. However, even with Sicily, it would still be difficult to assure predominant Greek influence, as there just might not be enough Greeks around that want to colonize that far.
 
Honestly, I can think of two major ways that also happen to be able to complement each other.

1) Earlier unification of the Greeks by a power interested in establishing colonies.
2) Major war that causes more displacement of Greeks than death.

These can compliment each other because you could have Greeks that flee overseas, and later move on to found other colonies, as well as a state that is interested in setting up colonies to spread their reach (and continue their Pan-Hellenic Unification)

To this end, I'd say you want some sort of Post-City State Reform in a much earlier period. Athens or Sparta could fit the bill, perhaps even Thebes. Heck, even a Phillip surviving scenario where he wins his war, only taking the Med from Persia. I think that latter one works best because it creates a more cohesive Empire, under a ruler that was already working on centralisation and could continue that path.

This then creates a situation where it's only Magna Grecia, Massilia, Emporion, Sicily, and perhaps parts of the Euxine that aren't under this Empires rule. Good solid targets, and once conquered, it makes sense to settle more loyal Greeks nearby to help keep it under control.

Heck, if we stick with Phillip, his and Alexanders willingness to adopt other cultures into their forces means that they're well places to recruit Celtiberians and Gauls into forces in the west. If that manages to not cause a revolt, it would spread the use of Greek and expand the economic reach of this Empire.
 
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