Atomic crystal structure affects the electromagnetic and thermal properties of common matter. Similarly, the nanoscale structure controls the properties of higher length-scale metamaterials, for example, nanoparticle superlattices and photonic crystals. Electrostatic self-assembly of oppositely charged nanoparticles has recently become a convenient way to produce crystalline nanostructures. However, understanding and controlling the assembly of soft nonmetallic particle crystals with long-range translational order remains a major challenge. Here, we show the electrostatic self-assembly of binary soft particle cocrystals, consisting of apoferritin protein cages and poly(amidoamine) dendrimers (PAMAM), with very large crystal domain sizes. A systematic series of PAMAM dendrimers with generations from two to seven were used to produce the crystals, which showed a dendrimer generation dependency on the crystal structure and lattice constant. The systematic approach presented here offers a transition from trial-and-error experiments to a fundamental understanding and control over the nanostructure. The structure and stability of soft particle cocrystals are of major relevance for applications where a high degree of structural control is required, for example, protein-based mesoporous materials, nanoscale multicompartments, and metamaterials.