<p>The ability to rearrange is crucial for the function of proteins and biopolymers and governs many properties of materials. While rearranging bonds are needed to create floppy structures, it has remained largely unexplored how they affect the self-assembly pathways. We here use a binary colloidal model system equipped with surface-mobile DNA-based bonds to study how regular structures with tunable flexibility and square network symmetry can be created through self-assembly. We find that reconfigurability during self-assembly leads to lattices with square symmetry which are inherently mechanically unstable and hence thermally floppy. By considering the role of size ratio, number ratio, and directionality induced by particle shape, we identify the pathways that maximize the yield and flexibility of these square lattices using a combination of experiments, analytical calculations, and simulations. Our study highlights the crucial role of reconfigurability in systems that are governed by enthalpic and entropic principles, from synthetic to biological, and might be useful for creating materials with novel or reconfigurable properties.</p>