Stainless steel (SS 304) is commonly employed in industrial applications due to its considerable corrosion resistance, thermal resistance, and ductility. Most of its intended applications require the formation of complex profiles, which justify the use of wire electrical discharge machining (WEDM). However, its high thermal resistance imposes a limitation on acquiring adequate surface topography because of the high surface tension of the melt pool, which leads to the formation of spherical modules; ultimately, this compromises the surface quality. Furthermore, the stochastic nature of the process makes it difficult to optimize its performance, especially if more than one conflicting response is involved, such as high cutting speed with low surface roughness and kerf width. Therefore, this study aimed to comprehensively investigate the interaction of SS 304 and WEDM, with a prior focus on simultaneously optimizing all the conflicting responses using the Taguchi-based grey relational approach. Analysis of variance (ANOVA) revealed that the current was the most significant parameter for cutting speed and kerf, whereas roughness, voltage (45%), drum speed (25.8%), and nozzle offset distance (~21%) were major contributing factors. SEM micrographs showed that optimal settings not only ensured simultaneous optimization of the conflicting responses but also reduced the number and size of spherical modules.