There were some monarchs traditions in Europe that predate the Roman Republic. Many of them were in Italy, but take Macedonia, Iskandar Megas came from there, and had been kings there for a very long time, and they continued to have Kings when the Diadochi period came. If we could somehow boost that Kingdom post-Diadochi to be able to hold off the Republic then that could be done.
Perhaps even butterfly the full conquest, Iskandar had a father, Phillip who was Hegemon, why not have him not die when he did, but lead the invasion. He wasn't interested in a fully Persian conquest, and might stop within Anatolia, Syria and Egypt. Then you have a new Empire that is "European", a Monarchy, and has both the ancient Egyptian monarch tradition, and those of Anatolia and Greece. That could at the very least set up SE Europe ideologically, and if they are dynamic and European rather than constantly in conflict with "Diadochi" to control Persia, they might well expand into Europe.
Heck, I'd say that is the right PoD - especially since we could see them focusing on uniting the Greeks, which includes parts of Southern Italia at the time - and it could very well conquer Italy and kill the Republican ideal in its crib.