A good way to force a chord progression to take an unexpected turn is to mess with a familiar open chord either by moving it up or down a fret (see the Am, B7, C shapes) or by lifting a finger off or putting one on (see the C+, Emadd9, D6, which originate as C, Em and D).
Here are some examples of chord shapes that belie their familiar looks with some unorthodox sounds…
