Intracellular condensates are highly multi-component systems in which complex phase behaviour can ensue, including the formation of architectures comprising multiple immiscible condensed phases. Relying solely on physical intuition to manipulate such condensates is difficult because of the complexity of their composition, and systematically learning the underlying rules experimentally would be extremely costly. We address this challenge by developing a computational approach to design pairs of protein sequences that result in well-separated multilayered condensates and elucidate the molecular origins of these compartments. Our method couples a genetic algorithm to a residue-resolution coarse-grained protein model. We demonstrate that we can design protein partners to form multiphase condensates containing naturally occurring proteins, such as the low-complexity domain of hnRNPA1 and its mutants, and show how homo- and heterotypic interactions must differ between proteins to result in multiphasicity. We also show that in some cases the specific pattern of amino-acid residues plays an important role. Our findings have wide-ranging implications for understanding and controlling the organisation, functions and material properties of biomolecular condensates.