Let me give you a million examples of multi-ethnic empires:
China, every single iteration of it
The chinese were usually not "multi-ethnic". Theirs has been a history of Han expansion wiping out (literally, those mountains in southern china once had their own distinct populations and cultures) all the natives they met, except for those capable of beating them in the battlefield (the northern nomads, and for a time).
yung.carl.jung said:
The Greek Empire at its peak
The Macedonians (Alexander apart, if we are to believe some ancient historians)
despised their subjects in the newly conquered lands. They made a point of not marrying with them,
yung.carl.jung said:
Europeans came to Africa. They established the "black race". Not one African had a saying in that. They also established the racial hierarchy. Blacks in Africa had no use for racism. They were never, ever united. Tribes and ethnicities were used as identification for them. Many things were associated with tribe and ethnicity. Race was an entirely meaningless concept for anyone but Europeans when it was invented.
The africans had no concept... isn't that the
noble savages thing? Africans without any agency, europeans just came to Africa and did things - no.
The reality is that africans were as much aware of
differences between them and the travelers from that other continent as the travelers were. That did not preclude trade, alliances, or war. What we now call "racism" as a concept is a 19th century development that was later projected backwards to apply to other somewhat similar attitudes regarding "different" foreign people, that got treated differently more due to religion and culture than skin color (which is not to say that skin color didn't play a part, as it became associated with cultural affinity expectations).
The single minded, obsessive focus on skin color, though, is a 19th century development. Slaves could be of any skin color, and many a "white european" became a slave in Africa roughly during the thousand years between 900 and 1900. It was indeed unusual for europeans to become enslaved in Europe, but that was because there existed an interdict against enslaving
christians there. White
pagans were fair game, but they became extinct early in the middle ages.
Slaves that converted to christianity posed a problem that early modern european societies argued a lot about. And so did the american natives, whether they were "pagan" and thus fair game, or ignorants of the true religions and thus
not fair game for enslavement...
Well, by "different races living together" I mean that quite literally. I realize that those empires contained different ethnic groups, but wasn't it the case that they lived in their own areas? For example, I don't think we would see a multi-racial city like London back then. Correct me if I'm wrong, but I don't think people really "immigrated" all that much back then and mostly kept to their "tribes".
I don't know about London. I do know that there were "multi-racial" (in our contemporary sense of "race") cities in the early modern age in Europe, as a result of the slave trade. You can see it in the paintings from the 17th and 18th centuries. The historical examples I know about are those of Lisbon. Slaves most definitely had an inferior social and legal status, in some matters horrifically so, and being mostly african (both black and moors) that status soon created a prejudice that associated their ethnic origin, recognizable by the skin color, with it. But there are records of indians, chinese, americans, turks, etc, as slaves during that period. The prejudices associated with such a (likely) origin did not
prevent africans and their descendants from being or becoming free citizens and and climbing the social ladder,
despite that prejudice. Skin color was not a barrier, culture was. A good example is a law from 1529 that orders "black women" to trade only by the doors of their masters instead of in the markets, but goes on to state that that there are many free black women in the city and exempts those from the prohibition. Thus, there was an association "black = slave", but also the recognition that even then there were already black non-slaves to whom legal discriminations should not apply.
Slaves were bough in to cities mostly to do the worst jobs, as the europeans that formerly did those jobs departed to risk their lives in colonial ventures. Migrations that in their purpose (not in the method) are not very removed from what goes on today in some "multi-cultural" cities. Later, as slavery was (gradually, slowly!) outlawed in Europe after the late-18th century, the freed slaves mingled with the inhabitants of the cities, their descendants becoming indistinguishable. But the process took some centuries, and started before the abolition. A rare qualifier regarding skin color in an 18th century legislative reasoning mentions "breeding slaves, some whiter than their owners" when deploring the continuation of slavery after the prohibition of slave imports. So this mix of "races" mostly happened before the pseudo-scientific "racial theories" showed up in the 19th century. I guess it would have been more difficult after those racial theories had taken hold.
Another interesting observation regarding "multi-cultural" life in early modern cities was the concert of chuch authorities with christianizing the imported slaves - now we talk about "integration" of immigrants. There were religious brotherhoods for providing mutual support, buying freedom and providing christian burials for their slave members, whatever the ethnic origin. There are also many parish records of intermarriage (and also concubinage, as the parishes complained of "sinful lives"...) between slaves of different ethnicities and between slaves and free citizens.
I am wondering off the original questions, so I'll end just by observing that slavery seems to me a very weird institution. I don't think it could have endured a few centuries in
urban settings anywhere without somehow being "normalized" into the life of the inhabitants of the city, allowing for a mingling and the slow erosion of slavery itself. But then I think of stuff such as caste systems, similar to slavery, that endured thousands of years in some places, so I really don't know...