Coiled-coil protein origami (CCPO) is a modular strategy for the de novo design of polypeptide nanostructures. CCPO folds are defined by the sequential order of concatenated orthogonal coiled-coil (CC) dimer-forming peptides, where a single-chain protein is programmed to fold into a polyhedral cage. Self-assembly of CC-based nanostructures from several chains, similarly as in DNA nanotechnology, could facilitate the design of more complex assemblies and the introduction of functionalities. Here, we show the design of a de novo triangular bipyramid fold comprising 18 CC-forming segments and define the strategy for the two-chain self-assembly of the bipyramidal cage from asymmetric and pseudo-symmetric pre-organised structural modules. In addition, by introducing a protease cleavage site and masking the interfacial CC-forming segments in the two-chain bipyramidal cage, we devise a proteolysis-mediated conformational switch. This strategy could be extended to other modular protein folds, facilitating the construction of dynamic multi-chain CC-based complexes.