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D&D 5ETurning Aasimar, Tiefling, Warforged, Shifter and similar races into multiclass templates that add onto "base" race instead of being separate race.
From what I've seen in theros you could make them a supernatural gift. There is essentially a gift that turns you into a warforged in the book. I see no reason why aasimar, tiefling, and genasi couldn't be the same. I've experimented with making them a feat which you have to take at 1st level (in games with bonus 1st level feats), but that's essentially the same as a supernatural gift.