Multi-tool aggregate unit (TU1) for a polishing head (H1) of an electronically-controlled polishing machine, for polishing edges of plates of stone material or synthetic material, for example for finishing operations in the mass production of kitchen tops or the like, said multi-tool aggregate unit (TU1) comprising: - a supporting structure for the multi-tool aggregate unit, - an aligned series of polishing tools which are rotatably mounted on said supporting structure of the multi-tool aggregate unit (TU1) and adapted to carry out progressively finer machining operations, the tools being arranged according to an order corresponding to the progression of the machining operation, with a tool for the most coarse machining operation which is arranged at one end of the series and a tool for the finest machining operation which is arranged at the opposite end, - wherein said supporting structure for the multi-tool aggregate unit (TU1) rotatably supports a single driving rotating shaft connected in rotation to all the tools by means of a mechanical transmission , said multi-tool unit (TU1) been characterized in that : - the multi-tool aggregate unit does not include a motor for actuating the rotation of the tools , - said driving rotating shaft has an end conical shank projecting from said supporting structure and configured to be removably connected in rotation within one end conical receptacle of a motorized spindle of said machining head, so that in the mounted condition of the multi-tool aggregate unit (TU1), said motorized spindle can drive in rotation all the tools of said multi-tool aggregate unit (TU1) while at the same time supporting the weight of said multi-tool aggregate unit (TU1), and - the supporting structure of the multi-tool aggregate unit (TU1) is configured to engage a spindle-supporting body (SP1) which supports the motorized spindle so as to prevent a rotation of the supporting structure of the multi-tool unit (TU1) around the axis of the spindle. - a supporting structure for the multi-tool aggregate unit, - an aligned series of polishing tools which are rotatably mounted on said supporting structure of the multi-tool aggregate unit (TU1) and adapted to carry out progressively finer machining operations, the tools being arranged according to an order corresponding to the progression of the machining operation, with a tool for the most coarse machining operation which is arranged at one end of the series and a tool for the finest machining operation which is arranged at the opposite end, - wherein said supporting structure for the multi-tool aggregate unit (TU1) rotatably supports a single driving rotating shaft connected in rotation to all the tools by means of a mechanical transmission , - the multi-tool aggregate unit does not include a motor for actuating the rotation of the tools , - said driving rotating shaft has an end conical shank projecting from said supporting structure and configured to be removably connected in rotation within one end conical receptacle of a motorized spindle of said machining head, - the supporting structure of the multi-tool aggregate unit (TU1) is configured to engage a spindle-supporting body (SP1) which supports the motorized spindle so as to prevent a rotation of the supporting structure of the multi-tool unit (TU1) around the axis of the spindle. <EOS>