If we did domesticate xenomorphs, we'd have to make artificial "hosts" for the facehuggers to implant an egg in. Since the xenos apparently incorporate some DNA from the host, we could even make custom ones!
Alien 3 already has one that came from an ox (or dog depending on which cut of the movie) so at least it doesn't need to be from people. Honestly aside from that they don't really get into the interesting DNA combination stuff too much. Could be cool for one that's like a breed of dog all specialized and whatnot.
Now I'm curious if a Chihuahua alien would be more aggressive than a regular Chihuahua or not
A Chihuahua alien would tremble, constantly, make quick jabs at its' victims then momentarily retreat before going in for another jab. All while barking incessantly.
Now I'm hopeful AI can help provide us with a Chihuahua edition of all the movies.