When I worked in adoption, I coined the phase "ambiguous ethnicity" to refer to individuals whose racial or ethnic identity was not clear cut to other people who saw them.

Some of these people may be of first generation mixed racial ancestry and some may not be. I know African Americans who "look White" and some of these individuals had a Black birthmother and a Black birth father. Usually their Black birthparents were both light skinned, but that was not always the case.

This is off topic from your point about "how far people [of multiple ethnic {I suppose you meant racial?] backgrounds hold on to one identity and drop the others, and how far do they try to keep them all in play?"

Here's my thoughts on that question:

Each racially mixed person has to find his or her way, hopefully by learning as much as they can about each of the cultures in their background, accepting & embracing both {all} of those backgrounds as part of his or her ancestry, and-preferably-directly experiencing as much as they can of these cultures.

However, what I am suggesting is that in the United States, if not in other countries, although an individual can self-identify his or her race for purposes of the census, public school enrollment, and other times, if this racial identity clashes with society's social definition of that race then that person is probably going to have considerable difficulties as a result of that decision.

For instance, in the United States, as far as I can tell, "White" has always been an exclusive race. If a person can be part-White and part some other race/ethnic group {such as Latino/a}, then that is a new development.

I have read about White Americans indicating that they have some American Indian ancestry, but this is often in geographical areas that don't have large populations of American Indians {and thus removed from the discrimination/racism against Native Americans}.

Let us say that a man has a known African American ancestor. My understanding is that would mean that this man would be considered African American, according to state laws and/or societal practices [I'm not clear if there still are laws that determine racial identity in the USA, but there certainly were such laws]. Let's say that this same man declared himself to be White. Let us also say that that man's skin color is brown and his hair texture is naturally tightly curled, meaning his skin color and hair texture is different than what American society has been told that White people look like. Will American society accept that he is White? If so, then the way American society views race has significantly changed.

That doesn't mean that the mixed race person who doesn't "look White" but has White ancestry, shouldn't assert that he is White.   Indeed, I have thought for some time that one way to end the strict definition of who is or is not White in the United States, is for a number of brown skinned first generation mixed adults to assert that they are White.

However, imo, those who would do this should be prepared for considerable static from White people {who would recognize this as a challenge to the traditional exclusive definition of who is White}. I also believe that persons who would do this would also get considerable static from non-White people who would interprete that racial identification as a rejection of that person's Black ancestry.

There are people struggling with this every day. This subject is much more than an intellectual discussion for them.