Multi-material additive manufacturing (AM) is a rapidly developing field that enables the production of parts designed with increased design freedom, to achieve superior performance compared to regular AM. Topology optimization (TO) is ideally suited to leverage the increased design freedom AM provides over conventional manufacturing methods, but resulting TO designs do not automatically conform to manufacturability limitations of AM, such as minimum feature size or maximum overhang angle. Existing single-material overhang filters and constraints cannot account for differences in critical overhang angle when applied to multi-material TO. This thesis proposes a novel multi-material overhang filter, that allows for independent control of the critical overhang angle of each material, and permits inter-material support. The filter's functionality is demonstrated for a compliance case, as well as for eigenfrequency optimization problems in both 2D and 3D. The filter accurately enforces the overhang angle for a wide range of critical angles, and can create printable designs without major performance loss.