The over-the-border private colonization of frontier areas during the Roman Empire hasn’t been taught in schools (gee, I wonder why?), but it led to an extension of the reach of Roman culture, politics, and maybe (for a time) the Latin language. In the 1990s a Roman fortified outpost was found in Ireland. It could have been a military station, perhaps dating from Agricola’s campaign in Scotland, or it may have been a privately-established trading post / colony. Or perhaps a combination of both (since the Roman army opened up areas for commerce as well as settlement). One unknown ancient entrepreneur brought a small colony of pottery makers from India, settled them on the Egyptian shore of the Red Sea (just as inviting and habitable then as now, I’m sure), and made fake-authentic Indian pottery to sell into the the seemingly boundless Roman market for Indian imports, thus saving him time and long voyages using the monsoon winds.
That makes a lot of sense to me. Look at how influential American culture, business, entertainment, etc. are in the world today. Roman influence would have been even more influential in its day in Europe.