Reconfigurability of two-dimensional colloidal crystal structures assembled by anisometric particles capable of changing their shape were studied by molecular dynamics computer simulation. We show that when particles change shape on cue, the assembled structures reconfigure into different ordered structures, structures with improved order, or more densely packed disordered structures, on faster time scales than can be achieved via self-assembly from an initially disordered arrangement. These results suggest that reconfigurable building blocks can be used to assemble reconfigurable materials, as well as to assemble structures not possible otherwise, and that shape shifting could be a promising mechanism to engineer assembly pathways to ordered and disordered structures.