D&D 5E (2014) Turning Aasimar, Tiefling, Warforged, Shifter and similar races into multiclass templates that add onto "base" race instead of being separate race.

[Vaalingrade]

Necro powers go!

Race as class!

Race as class!

Please never again.

 

[cbwjm]

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.

 

[Minigiant]

I already have a premise for my Paragon class that does this.

It doesn't do Aasimar, Tiefling, etc but it goes more into the origin and power source route.

So you got Noble Descendant (Martial), Demigod (Divine), Alchemical Soldier (Arcane), Lycantrope (Primal), Vampire (Shadow), Feyblade (Fey) or Earth Warrior (Elemental)

 

[Parmandur]

Notably, the way Genasi and Aasamir are reinvented in Monsters of the Multiverse basically does this.