I would say 1) each major racial category in the US can be further subdivided into multiple ethnicities, 2) different combinations of ethnicities can be considered their own ethnicities (e.g. Mexican + Iranian is different from ADOS + Japanese), and that 3) mixed-race people effectively constitute a separate ancestry group from the major racial categories.
Points 1 and 2 are more relevant for groups that are of relatively recent immigrant origin and are thought of as more culturally distinct. Italians, Polish, and Jews are more widely thought of as distinct Non-Hispanic White ethnicities than say Irish, Germans, or Dutch.
Points 2 and 3 imply that integration/assimilation of immigrants and their children results in ethnic identity becoming replaced with a more racialized identity that corresponds to long-standing US Census racial categories. Within my predominantly nonwhite RL social network, and I've seen this happen as many people end up partnered with members of the same race but not necessarily of the same ethnicity. The Puerto Rican chick born and raised on the island marries a Chicano guy from Washington state. The children of Indian immigrants who end up with other Subcontinentals don't particularly care about caste or heritage language unless they're Punjabi Sikh.
The children of the East and Southeast Asian diasporas intermingle amidst an evolving pan-diasporic subculture of weeaboo-ism, koreaboo-ism, and 88rising. African immigrants and their children own their blackness and identify with it on uniquely American terms. Et cetera.
My ethnic identity is Chinese. My racial identity is East/Southeast Asian. I don't think of myself as "different" from other Chinese Americans whose families are from different parts of China as mine (or from Taiwanese or Hong Kong diasporans in the US) because we are all seen as Chinese and as East/Southeast Asian by the broader American public. These are two of many aspects of my personal identity, and they are unlikely to change because I have a fairly fixed concept of what "ethnicity" and "race" mean.