The tyrannoi of Syracuse had an influence outside of Sicily at their peak! Dionysius I of Syracuse held sway over most of Sicily, and ports in Magna Graecia - southern Italy - such as Kroton and Locri. In addition, Dionysius recruited Gallic mercenaries from the northern Adriatic (Senones), supported Greek enclaves in northern Italy (Spina) and the Adriatic Sea (Lissus & Pharos), and was an ally of Sparta.

King Agaothcles of Sparta also sought to dominate southern Italy, and made alliance with the Bruttians so as to dominate Kroton and Locri. And he famously sought to overrun Carthage and Libya in alliance with Ophellas - the ptolemaic governor of Kyrene...

So at its peak, the tyrants of Sicily were super-powers of the central Mediterranean.

H.