Biomolecular complexes can form stable assemblies yet can also rapidly exchange their subunits to adapt to environmental changes. Simultaneously allowing for both stability and rapid exchange expands the functional capacity of biomolecular machines and enables continuous function while navigating a complex molecular world. Inspired by biology, we design and synthesize a DNA origami receptor that exploits multivalent interactions to form stable complexes that are also capable of rapid subunit exchange. The system utilizes a mechanism first outlined in the context of the DNA replisome, known as multisite competitive exchange, and achieves a large separation of time scales between spontaneous subunit dissociation, which requires days, and rapid subunit exchange, which occurs in minutes. In addition, we use the DNA origami receptor to demonstrate stable interactions with rapid exchange of both DNA and protein subunits, thus highlighting the applicability of our approach to arbitrary molecular cargo, an important distinction with canonical toehold exchange between single-stranded DNA. We expect this study to benefit future studies that use DNA origami structures to exploit multivalent interactions for the design and synthesis of a wide range of possible kinetic behaviors.