Increasing demands in modern production pose new challenges to established forming processes. One approach to meet these challenges is the combined use of established process classes such as sheet and bulk forming. This innovative process class, also called sheet-bulk metal forming (SBMF), facilitates the forming of minute functional elements such as lock toothing and gear toothing on sheet-metal bodies. High tool loads and a complex material flow that is hard to control are characteristic of SBMF. Due to these challenging process conditions, the forming of functional elements is often insufficient and necessitates rework. This negatively affects economic efficiency. In order to make use of SBMF in industrial contexts, it is necessary to develop measures for improving the forming of functional elements and thereby push existing forming boundaries. This paper describes the design and numerical replication of both a forward and a lateral extrusion process so as to create involute gearing in combination with carrier teeth. In a combined numerical-experimental approach, measures for extending the die filling in sheet-metal extrusion processes are identified and investigated. Here, the focus is on approaches such as process parameters, component design and locally adjusted tribological conditions; so-called 'tailored surfaces'. Based on the findings, fundamental mechanisms of action are identified, and measures are assessed with regard to their potential for application. The examined approaches show their potential for improving the forming of functional elements and, consequently, the improvement of geometrical accuracies in functional areas of the workpieces. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.