This paper seeks to advance the design of planar multiloop shape-changing mechanisms used in a variety of applications, such as morphing extrusion dies and airfoils. The presence of defects is a limiting factor in finding suitable single-degree-of-freedom (DOF) morphing mechanisms, particularly when the number of shapes to achieve is large and/or the changes among those shapes are significant. This paper presents methods of designing multi-DOF mechanisms to expand the design space in which to find suitable defect-free solutions. The primary method uses a building block approach with Assur group of class II chains, similar to the current 1-DOF synthesis procedure. It is compared to both the 1-DOF procedure and an alternative multi-DOF procedure that generates mechanisms with single-DOF subchains. In all cases, a genetic algorithm is employed to search the design space. Two example problems involving four prescribed shapes demonstrate that mechanisms exhibiting superior shape matching are achieved with the primary multi-DOF procedure, as compared to the other two procedures.