It sounds like there are 2 different scenarios mixed together here:
1) An individual has multiple races (as described in the original question). The solution described here does "solve the problem" in that one assigns a "mixed race" concept that means the CDM can be used as is. Having said that, if I were to ask "give me all persons of African American race", persons who were of "mixed race" (say African American and Asian) would not be selected from the person table. This is a very challenging problem to address in a robust manner (eg, in graphs), so it may just be a "punt" to the user to have to handle it.
2) There are multiple events where a person's race is recorded. In this situation, Erica's suggestion about the date stamp of the recording of the race makes sense in that setting. This is opposed to the view where we are making assertions about the inferred state at conception also described here. It depends on the type of data sources it seems. In the AoU setting, we have different "tiers" of data sources, so I doubt we'll use the "most recent" approach to resolve this. We will take the most recent of X>Y>Z, where X, Y, and Z are different data sources depending on what is available for that individual (or something along those lines).
From my perspective, it would be nice if the Person table could support something more than just "Mixed Race" for these situations, but building out such a solution is complicated (does one create as concepts as there are combinations?).