Constructing hierarchical superstructures to achieve comparable complexity and functions to proteins with four-level hierarchy is challenging, which relies on the elaboration of novel building blocks with complex structures. We present a series of catenated cages with unique structural complexity and tailorability. The rational design was realized as such: A catenane of two symmetric cages (CSC), CSC-1, with all rigid imine panels was converted to a catenane of two dissymmetric cages (CDC), CDC-1, with two exterior flexible amine panels, and CDC-5 was tailored from CDC-1 by introducing an additional methyl group on each blade to increase lateral hindrance. CDC-1s with the most irregular and flexible configuration formed supramolecular dimers, which self-organized into 3D continuous wavelike plank with a three-level hierarchy, previously undiscovered by conventional building blocks. A drastically different 3D triclinic crystalline phase with a four-level hierarchy and trigonal phase with a three-level hierarchy were constructed of distorted CSC-1s and the most symmetric CDC-5s, respectively. The wavelike plank exhibited the lowest order, and the triclinic phase had a lower order than the trigonal phase which had the highest order. It correlates with the configuration of the primary structures, namely, the most disordered shape of CDC-1, the low-order configuration of CSC-1, and the most ordered geometry of CDC-5. The catenated cages with subtle structural differences therefore provide a promising platform for the search of emerging hierarchical superstructures that might be applied to proton conductivity, ferroelectricity, and catalysis.