A gear change device for a motor vehicle includes at least one primary shaft (P) and at least one secondary shaft (S), which have end portions (P1, S1) on the side opposite to the engine that extend beyond respective rolling bearings (C2, C4) and carry at least one gear pair (R51, R52). The end portions (P1, S1) of the primary and secondary shafts (P, S) are configured for being coupled to respective shaft-extension elements (E1, E2), which carry a further gear pair (R61, R62). The shaft-extension elements (E1, E2) are not mounted when it is desired to obtain a gear change device with n gears, whereas they are mounted when it is desired to obtain a gear change device with at least n+1 gears. Interference-fitted on the coupled parts are cylindrical bushings (B1, B2) that ensure coaxiality of the shaft-extension elements (E1, E2) with the primary and secondary shafts (P, S) and consequent proper meshing of the gear pairs (R51, R52; R61, R62) carried thereby.