A supporting frame for motor-vehicle bodyshells comprising: - a first pair of supports, the supports of said first pair having a first orientation (Z, Z10) with respect to said frame and being spaced apart in a transverse direction of said frame; - a second pair of supports and at least one third pair of supports, which are configured for co-operating alternatively with said first pair of supports for receiving a motor-vehicle bodyshell, said second pair of supports and at least one third pair of supports being arranged in positions spaced apart, in a longitudinal direction of said frame, from said first pair of supports, wherein: - the second pair of supports and the third pair of supports are carried by an auxiliary frame, which is rotatable about a transverse axis between a first operating position and a second operating position; - in the first operating position, the auxiliary frame positions the second pair of supports according to the first orientation (Z, Z12) with respect to the frame and so that it is longitudinally spaced apart from the first pair of supports by a first longitudinal distance, while the third pair of supports is positioned with a second orientation with respect to the frame; and - in the second operating position, the auxiliary frame positions the third pair of supports according to the first orientation (Z, Z14) with respect to the frame and so that it is longitudinally spaced apart from the first pair of supports by a second longitudinal distance, while the second pair of supports is positioned with a third orientation with respect to the frame, the supporting frame being characterized in that said auxiliary frame comprises a cross member, which extends in a transverse direction with respect to said frame and is rotatably supported (20, 22) with respect thereto, said cross member bearing at respective opposite ends a first plate and a second plate, each of which carries a support of the second pair of supports and a support of the third pair of supports arranged on opposite sides of the respective plate (24, 26), in that it further includes, for each plate (24, 26) of the auxiliary frame, a first stop element configured for exerting an action of contrast in regard to said plate (24, 26, M1) when the auxiliary frame is in the second operating position, and a second stop element configured for exerting an action of contrast in regard to said plate (24, 26, M2) when the auxiliary frame is in the first operating position, and in that each plate (24, 26) includes a rectilinear main portion, a first bracket and a second bracket, which project in a transverse direction on opposite sides of the main portion, said first bracket being configured to bear upon said first stop element, and said second bracket being configured to bear upon said second stop element. - a first pair of supports, the supports of said first pair having a first orientation (Z, Z10) with respect to said frame and being spaced apart in a transverse direction of said frame; - a second pair of supports and at least one third pair of supports, which are configured for co-operating alternatively with said first pair of supports for receiving a motor-vehicle bodyshell, said second pair of supports and at least one third pair of supports being arranged in positions spaced apart, in a longitudinal direction of said frame, from said first pair of supports, - the second pair of supports and the third pair of supports are carried by an auxiliary frame, which is rotatable about a transverse axis between a first operating position and a second operating position; - in the first operating position, the auxiliary frame positions the second pair of supports according to the first orientation (Z, Z12) with respect to the frame and so that it is longitudinally spaced apart from the first pair of supports by a first longitudinal distance, while the third pair of supports is positioned with a second orientation with respect to the frame; and - in the second operating position, the auxiliary frame positions the third pair of supports according to the first orientation (Z, Z14) with respect to the frame and so that it is longitudinally spaced apart from the first pair of supports by a second longitudinal distance, while the second pair of supports is positioned with a third orientation with respect to the frame,