> Is it “it may be possible but the tech isn’t there” or “fundamentally, it is not possible”?

For a god it may be possible, for us, not so much. For comparison it's like modifying a program in a language we don't understand. This program has grown randomly over aeons and the strangest things relate to each other. You're basically stuck with randomly changing things and seeing what happens. But since people mature so slowly that's very slow progress.

During the maturation process of a foetus, there's lots of little tripwires to abort if something weird is going on.

That said, if you find some baby born with gill like structures or four arms, if you sequence them you might get a head start. But the slow testing phase will be a problem.

Evil science fiction villain mode: unless of course we figure out how to grow foetuses into babies without a woman being involved, you could build a factory to test 100,000 variations all at once. That would speed it up a bit.