This is explicitly prohibited in the rules. You may have many ancestries, but the one you identify with primarily is your Heritage.
Versatile Heritages Advanced Player's Guide pg. 28
Though a character can have only one heritage, it doesn't mean characters with lineages tracing back to multiple ancestries or heritages don't exist. It's certainly possible for a dhampir to be born to a half-elf mother, or for a duskwalker to appear in a community of death warden dwarves. In these cases, the influence of the versatile heritage overshadows the other heritage—the dhampir heritage overshadows the half-elf heritage, and the duskwalker abilities replace those of the death warden dwarf heritage. So while, superficially, a character might bear a resemblance to both heritages, mechanically, they only gain the benefits of the versatile heritage.
From the same page:
Since a versatile heritage is a heritage, you can have only one, and you can't have any other heritage in addition to your versatile heritage.
Sometimes a versatile heritage might give you an ability that conflicts with an ability from your ancestry. In these cases, you choose which of the conflicting abilities your character has.
In the example case, the half-elf character selecting an elven heritage through an ancestry feat prohibits themselves from taking an aasimar or tiefling heritages through any other means.
There isn't even much of a mechanical benefit even if you could overlap heritages, since many aasimar heritage benefits can be done through elven ancestries. Not quite as much overlap with tiefling, but still a good chunk of overlap.
Roleplay wise... Just go ahead and say you are decended from a Celestial or Devil or whatever. Even without mechanic changes, it lands squarely under the Rule of Cool, and can add some interesting plot hooks if your DM plays on that. Who knows? You may be gaining class features as a cleric, oracle, or witch by tapping into that supernatural ancestry while retaining your elven heritage.