The US is rapidly becoming a multi-ethic society. These are also always much more violent than homogenous societies.
The Americas were "multi-ethnic" before the arrival of Europeans
No country in the Americas has ever been "mono-ethnic" or "mono-cultural." Rather, in every American society, one culture has dominated. This is no less true in Europe, either. European is definitely not an ethnicity. French isn't one either. The argument that France, Spain or Italy are homogeneous culturally is false. What is true is that different ethnic cultures are considered as being historically linked. England became multi-ethnic with the invasion of the Romans, and later the Norsmen, then the Normans, not to mention the Jutes, Picts and Danes.
Cultural dominance may be inevitable. But, this country has always been multi-cultural. Any American who doesn't think so obviously doesn't listen to the blues, eat Chinese food, do Asian martial arts, eat pizza, or yams, or corn, and the list goes on. In fact, Americans are the most multi-cultural of peoples. They'll have scones and croissants and biscuits and corn bread for breakfast, and never think they're doing anything "un-American."
Otoh, it's true that it's unlikely that "Americans" will think of themselves as one people or "e pluribus unum" and all that other pc bs.
Not even the Pilgrims were the same in terms of class, ethnicity or religion. That's why they made the Mayflower Compact:
In the name of God, Amen. We, whose names are underwritten, the loyal subjects of our dread Sovereign Lord King James, by the Grace of God, of Great Britain, France, and Ireland, King, defender of the Faith, etc.
Having undertaken, for the Glory of God, and advancements of the Christian faith and honor of our King and Country, a voyage to plant the first colony in the Northern parts of Virginia, do by these presents, solemnly and mutually, in the presence of God, and one another, covenant and combine ourselves together into a civil body politic; for our better ordering, and preservation and furtherance of the ends aforesaid; and by virtue hereof to enact, constitute, and frame, such just and equal laws, ordinances, acts, constitutions, and offices, from time to time, as shall be thought most meet and convenient for the general good of the colony; unto which we promise all due submission and obedience.
In witness whereof we have hereunto subscribed our names at Cape Cod the 11th of November, in the year of the reign of our Sovereign Lord King James, of England, France, and Ireland, the eighteenth, and of Scotland the fifty-fourth, 1620.[13]
Of course, there were people of different ethnicities living in Jamestown before the Pilgrims arrived.