The power of natural evolution lies in the adaptability of biological organisms but is constrained by the time scale of genetics and reproduction. Engineeringartificial molecular machines should not only include adaptability as a core feature but also apply it within a larger design space and at a faster time scale. A lesson from engineering electromechanical robots is that modular robots can perform diverse functions through self-reconfiguration, a large-scale form of adaptation. Molecular machines made of modular, reconfigurable components may form the basis for dynamic self-reprogramming in future synthetic cells. To achieve modular reconfiguration in DNA origami assemblies, we previously developed a tile displacement mechanism in which an invader tile replaces another tile in an array with controlled kinetics. Here, we establish design principles for simultaneous reconfigurations in tile assemblies using complex invaders with distinct shapes. We present toehold and branch migration domain configurations that expand the design space of tile displacement reactions by two orders of magnitude. We demonstrate the construction of multitile invaders with fixed and variable sizes and controlled size distributions. We investigate the growth of three-dimensional (3D) barrel structures with variable cross sections and introduce a mechanism for reconfiguring them into 2D structures. Last, we show an example of a sword-shaped assembly transforming into a snake-shaped assembly, illustrating two independent tile displacement reactions occurring concurrently with minimum cross-talk. This work serves as a proof of concept that tile displacement could be a fundamental mechanism for modular reconfiguration robust to temperature and tile concentration.