Natural overtones aren't really something you can "dial in." You can do certain things to enhance them or bring them out in an instrument (or foul them) but it's not something you can control a whole lot. They're a byproduct of the resonance and tonal properties of your instruments, mainly your guitar and your amp.
It sound like you're trying to make chords other than power chords sound good. My first suggestions would be to use less gain overall, brighten your tone a bit, and make sure your intonation is true and your guitar is in tune.