The use of CNC equipment that integrates several machining operations eliminates downtime due to changes in setup and clamping of workpieces in more than one machining device. A review of CNC equipment and tools known from the literature and from manufacturers' offerings indicates that new technical solutions are being developed to integrate two or more technological operations. However, these examples have numerous limitations and are mostly not suitable for machining surfaces with complex shapes. An example of such solutions is the use of a dual-tool grinding head, which integrates the process of rough grinding with a ceramic grinding wheel and finish grinding with a flexible grinding wheel. Unfortunately, it has the disadvantage of being limited by the angular shape of the ceramic grinding wheel, making it unable to adapt to the complex geometries of the shaped surfaces being ground. The need to overcome this limitation became the motivation for the research work described in this article. By means of experimental research, it was verified what effect the radial outline on the periphery of a ceramic grinding wheel realized by rough grinding would have on the surface roughness parameters obtained in the process of grinding shaped surfaces. For this purpose, grinding processes using a ceramic wheel with a conical and radial outline were compared. The result of the study was a summary of the surface roughness parameters Sa, St, Sq, Spk, Str, and Sds obtained after two-stage machining (rough and finish grinding). The obtained analysis results showed that changing the axial outline of the ceramic grinding wheel makes it possible to significantly expand the range of applications of the dual-tool head without negatively affecting the quality of the machined surface. Thus, such an improvement will make it possible to increase the applicability of the head by grinding shaped surfaces with a radial profile of curvature.