Halftoning by screening is a popular technique because of its computational simplicity. The screen matrix is very determining for the quality of the generated halftone patterns. In this paper we will introduce a novel screen design framework for the generation of multilevel AM halftoning screens. A first important novelty is the support for multilevel screens. The screen design is targeted towards multilevel electrophotographic print technologies, where the intermediate output levels are not as reproducible as the outer levels. In this case it is important to control the so called hardness of the screen, which comes down to the fraction of pixels with intermediate levels in the halftone patterns. In the proposed algorithm we can control this hardness directly. Another novelty is that the framework isn't limited to the classical orthonormal AM halftoning grids. The geometrical foundation of the algorithm is based on the concept of Voronoi tessellation. This approach makes it possible to handle for example slanted AM grids or grids with different ruling in the main directions.