The three position selector switch may actually be set up as:
- Single pickup
- Humbucking configuration
- Out of phase configuration
These three sound dramatically different. The out of phase configuration cancels a lot of tones and accentuates some higher tones. Some describe it as thinner/jangly/cutting through. I use it on one of my guitars for a bit of dynamic range - changing from the fat Humbucking sound to a piercing cut through accentuating pick and finger noise, as well as some harmonics.
According to this page, however, Avril's guitar is set up as:
So this will still give you a range of sounds, just not that different. Moving the effective pickup position by a small amount will affect some of the higher harmonics, specifically.