There is one large group of immigrants that refused to assimilate and one noteworthy small group as well. The first failed completely over a 200 year period and the second succeeded.
The first are Roman Catholics who came from France, Ireland, England, Italy, Poland and most recently from Mexico. For two hundred years Roman Catholics of every ethnicity have set up their own private school system, hospitals, burial societies and often their own Universities. Fortunately for the rest of America, this tenacious 25% of our population failed in their separatist efforts. It is impossible to think of Roman Catholics in America as a distinct unassimilated population. They aren’t. They failed.
The group that succeeded are the Amish. They did it, for over 200 years, by completely separating themselves from the mainstream society and making it clear to young members that a point would come in their lives when they would either openly join the Amish unreservedly or leave. It worked. They have not disappeared and they have not been assimilated.
The lesson is: everyone that is in America assimilates. To avoid assimilation live disconnected from America in isolation. Addendum: don’t be too antagonistic, the Mormons did and America sent an army to assimilate the Mormons.