Engineered variants of the capsid-forming enzyme lumazine synthase can exploit electrostatic interactions to encapsulate complementarily charged guest macromolecules. Here we investigate the effect of ionic strength and cargo molecules on assembly of AaLS-13, a negatively supercharged lumazine synthase protein cage, and we show that multishell structures are produced upon mixing the capsid core with free capsomers and a positively supercharged variant of the green fluorescent protein GFP(+36). The assembly process is mediated by favorable electrostatic interactions between the negatively charged capsid shells/capsomers and GFP(+36) molecules, and it is therefore strongly dependent on ionic strength. The mechanism of formation of these assemblages is likely similar to the assembly of multishell structures of some virus-like particles, where outer shells organize as nonicosahedral structures with larger radii of curvature than the templating inner shell. In contrast to the viral multishell structures, the positively charged mediator was found to be essential for the assembly of multilayered structures of different shapes and sizes constituted of AaLS-13 capsomers. This mediator-bridging approach may be widely applicable to create protein-based hierarchical nanostructures for various nanotechnology applications such as drug delivery and bioimaging.