A tool system for machining includes a tool body that has a first end for connecting to a machine tool and a second end having an end face on which a seat for an interchangeable cutting insert is formed. The cutting insert has an underside formed as an abutment surface, a top side formed as a rake face, and an encircling side face formed as a flank, and a cutting edge is formed at a transition from the top side to the encircling side face. The cutting insert is arranged on the seat such that the top side extends perpendicularly to the longitudinal axis of the tool body and the cutting edge protrudes beyond the outer circumference of the end face of the tool body in a radial direction with respect to the longitudinal axis with two usable cutting corners and cutting-corner portions adjoining the latter on both sides.