You can do it but the person will look like a freak. The key in your post is "natural face". An exact duplicate will be a challenge to look natural. You'll need to add some irregularities to help achieve this like editing out moles or destinct marks from at least one side or other.
So many studies have been done on face symmetry and attractiveness. Symetric faces are universally seen as more attractive but when taken to the extreme and perfect symmetry is achieved (exactly what you're talking of doing) the results are not favorable.
Couple of examples from a Penn State study a few years ago with perfect symmetry: