Certainly, as does everybody, all the way down to the core family level. Persons make up families, which make up clans, which make up tribes, which make up nations, which make up races. You are part of subdivisions within subdivisions, by heritage. Different persons give different value to each subdivision - or no value to them at all.

The native Americans would absolutely consider themselves as more similar to each other than to the European and African arrivals. Just by matter of undeniable physical features.

As for the Romans, it is within the mists of history and mythology (Rape of the Sabine Women), but nobody can deny that there was an original people there in Italy, and other peoples who became citizens and/or subjects of Rome weren't ethnically Roman.