Dynamic protein-rich intracellular structures that contain phase-separated intrinsically disordered proteins (IDPs) composed of sequences of low complexity (SLC) have been shown to serve a variety of important cellular functions, which include signalling, compartmentalization and stabilization. However, our understanding of these structures and our ability to synthesize models of them have been limited. We present design rules for IDPs possessing SLCs that phase separate into diverse assemblies within droplet microenvironments. Using theoretical analyses, we interpret the phase behaviour of archetypal IDP sequences and demonstrate the rational design of a vast library of multicomponent protein-rich structures that ranges from uniform nano-, meso- and microscale puncta (distinct protein droplets) to multilayered orthogonally phase-separated granular structures. The ability to predict and program IDP-rich assemblies in this fashion offers new insights into (1) genetic-to-molecular-to-macroscale relationships that encode hierarchical IDP assemblies, (2) design rules of such assemblies in cell biology and (3) molecular-level engineering of self-assembled recombinant IDP-rich materials.