Lyric discussion by mimesaresexy 

Cover art for Ampersand lyrics by Dresden Dolls, The

My guess is that it has something to do with Romeo & Juliet. I think that what she means by not living on one side of an ampersand is that she doesn't want to forever be known as part of a duet. For instance, most people hear Juliet and think Romeo & Juliet, not just Juliet.