Wire Electrical Discharge Turning (WEDT) is a unique adaption of the Wire Electrical Discharge Machining (WEDM) process and enables one to generate precise 3-D axis-symmetric profiles on electrically conductive materials irrespective of their hardness. In the present study, profile geometries like spherical, cylindrical, and taper are generated on the same workpiece to create a combined-shape structure. The effect of parametric settings on Volumetric Error (VE), Roundness (Ront), Average Surface Roughness (Ra), and Volumetric Material Removal Rate (VMRR) is investigated for the above-said geometries based on Response Surface Methodology (RSM). Experimental results show that the volumetric or geometric error is maximum for spherical and minimum for cylindrical turned surfaces. The roughness of the cylindrical part is better as compared to the spherical and tapered surfaces. A minimum roundness value of 28.19 µm for the spherical, 11.80 µm for the cylindrical, and 26.25 µm for the taper-turned surfaces has been observed. The VMRR of the cylindrical part was found to be higher than that of spherical and tapered parts. FESEM has been utilized to study the surface integrity of the geometries machined by WEDT, and a recast layer was observed in all three cases.