The design of structures presents a number of complex design challenges that can be effectively well addressed using the material layout and material selection capabilities of structural Topology Optimization (TO). However, a significant portion of research in the field of TO is focused on cases of maximum stiffness design for structures subjected to externally applied mechanical loads. Nevertheless, controlling stresses within a structure is of paramount concern, as they are a primary consideration in any design problem. Thus, stresses have received more attention recently in optimization problem formulations, as also addressed in this work. The multi-material design setting offers additional design freedom which can lead to structures with lower stress levels compared to the single-material case. The present work is focused on multi-material stress-based TO. Specifically, the maximum von Mises stress is minimized under compliance and volume fraction constraints inside a design domain through topology changes and material selection. Two solid materials are mixed amidst void to generate an advanced composite, i.e., a Functionally Graded Material (FGM). In order to completely explore the FGM potential in stress mitigation, one aims here to extend the FGM solution to the full-design domain, such that a uniformly stressed structure is favoured. For comparison purposes, the present work also applies TO to the design of classical composites characterized by discrete material phases separated by sharp interfaces. Since the present work is focused on the optimal design of structures mixing isotropic solids, one chooses to use a material model based on the Hashin-Shtrikman (HS) bounds for the elastic moduli of isotropic composite materials. Consequently, the well-known RAMP interpolation scheme is used to interpolate among two solid materials, noticing that it adequately renders the HS bounds. This way it is possible to capture the physics of mixtures considering the FGM’s mechanical properties. The stress-based formulation is applied to a set of benchmarks, typically beam and plate type structures in plane stress with force/displacement-based boundary conditions. Parallel computing is used to reduce optimization time-costs. The results obtained show how the multi-material designs outperform the single-material ones. FGM designs are associated with the lowest stress levels, since they typically approximate a fully stressed design.