Method for producing a multicoat paint system (M) on a metallic substrate (S), comprising producing a cured electrocoat (E.1) on the metallic substrate (S) by electrophoretic application of an electrocoat (e.1) to the substrate (S) and subsequent curing of the electrocoat (e.1), producing (2.1) a basecoat (B.2.1) or (2.2) a plurality of directly successive basecoats (B.2.2.x) directly on the cured electrocoat (E.1) by (2.1) applying an aqueous basecoat material (b.2.1) directly to the electrocoat (E.1) or (2.2) applying a plurality of basecoat materials (b.2.2.x) in direct succession to the electrocoat (E.1), producing a clearcoat (K) directly on (3.1) the basecoat (B.2.1) or (3.2) an uppermost basecoat (B.2.2.x) by applying a clearcoat material (k) directly to (3.1) the basecoat (B.2.1) or (3.2) the uppermost basecoat (B.2.2.x), jointly curing (4.1) the basecoat (B.2.1) and the clearcoat (K) or (4.2) the basecoats (B.2.2.x) and the clearcoat (K), characterized in that the basecoat material (b.2.1) or at least one of the basecoat materials (b.2.2.x) comprises at least one aqueous dispersion comprising at least one copolymer (CP), said copolymer (CP) being preparable by (i) initially charging an aqueous dispersion of at least one polyurethane, and then (ii) polymerizing a mixture of olefinically unsaturated monomers in the presence of the polyurethane from (i), in which (a) a water-soluble initiator is used, (b) the olefinically unsaturated monomers are metered in such that a concentration of 6.0% by weight, based on the total amount of olefinically unsaturated monomers used for polymerization, in the reaction solution is not exceeded over the entire reaction time, and (c) the mixture of the olefinically unsaturated monomers comprises at least one polyolefinically unsaturated monomer. producing a cured electrocoat (E.1) on the metallic substrate (S) by electrophoretic application of an electrocoat (e.1) to the substrate (S) and subsequent curing of the electrocoat (e.1), producing (2.1) a basecoat (B.2.1) or (2.2) a plurality of directly successive basecoats (B.2.2.x) directly on the cured electrocoat (E.1) by (2.1) applying an aqueous basecoat material (b.2.1) directly to the electrocoat (E.1) or (2.2) applying a plurality of basecoat materials (b.2.2.x) in direct succession to the electrocoat (E.1), producing a clearcoat (K) directly on (3.1) the basecoat (B.2.1) or (3.2) an uppermost basecoat (B.2.2.x) by applying a clearcoat material (k) directly to (3.1) the basecoat (B.2.1) or (3.2) the uppermost basecoat (B.2.2.x), jointly curing (4.1) the basecoat (B.2.1) and the clearcoat (K) or (4.2) the basecoats (B.2.2.x) and the clearcoat (K), (i) initially charging an aqueous dispersion of at least one polyurethane, and then (ii) polymerizing a mixture of olefinically unsaturated monomers in the presence of the polyurethane from (i), in which (a) a water-soluble initiator is used, (b) the olefinically unsaturated monomers are metered in such that a concentration of 6.0% by weight, based on the total amount of olefinically unsaturated monomers used for polymerization, in the reaction solution is not exceeded over the entire reaction time, and (c) the mixture of the olefinically unsaturated monomers comprises at least one polyolefinically unsaturated monomer. (a) a water-soluble initiator is used, (b) the olefinically unsaturated monomers are metered in such that a concentration of 6.0% by weight, based on the total amount of olefinically unsaturated monomers used for polymerization, in the reaction solution is not exceeded over the entire reaction time, and (c) the mixture of the olefinically unsaturated monomers comprises at least one polyolefinically unsaturated monomer. <EOS>