TL;DR: The 2020 US Census shows a very large increase in the “Two or More Races” group. However, at least some of this likely has to do with changes in the question design and coding procedures, and shifting constructions of race.
The US Census construction of Race
When the US Census asks about race and ethnicity, it tries to reflect the way that racial/ethnic identity is constructed in the United States, but it also has to obey certain constraints. As a result there are some outstanding differences between race as it is constructed by US residents, and race as it is constructed by the US Census. For example, Middle Eastern Americans often do not identify as White, and are not perceived as White (and I suspect this perception has increased since 9/11), but in the US Census they are still classified as white.
Another outstanding difference is in how the US Census defines “race” vs “ethnicity”. According to the Census, “Hispanic, Latino, or Spanish origin” and its negation are the only ethnic categories, and are excluded from the racial categories. I can say from my own experience with surveys, that this system is really weird, and causes no end of confusion among respondents.