The system (20) has a tool carrier unit (24) arranged in a tool carrier base (22). The tool carrier base and a workpiece spindle (10) of a machine tool are movable relative to each other for processing a workpiece. Another tool carrier unit (90) is arranged with a tool carrier body (102) running in an extending direction and form a tool carrier element (98) at the tool carrier base. A tool receiver unit for a rotatably fixed tool is arranged at the body and moved into a processing position by moving the body in the direction relative to the tool carrier base.
