I have very big doubts on how multicultural a nation can be while also being democratic. The issue is, in a democracy, how much power any group has is dependent on their population. Which creates an incentive for some groups to discriminate against other groups to maintain power.
Throwing immigration into the mix really fucks things as now, you have rapid demographic changes that upset an existing power balance. It makes it to where immigration policy as a whole turns into a proxy battle for which group has the most power.
Ultimately countries as big and diverse as the US tend to fall into autocracy. As that ends up being the only way all these differing people can be united.
That is probably what will happen to the United States, as the only group that cares about the founding ideals of the nation, the centrist democrats, seem to be hated by both the right and the left. The right wants fascism, while the left wants socialism. While fascism and socialism are not the same thing, they both seek to tear down the existing systems in America.