Dyeing keratin fibers, preferably human keratin fibers such as hair, comprises: treating the fibers with cosmetic compositions containing, taken together or separately in the composition, ingredients comprising e.g. ortho-diphenol derivatives, manganese salts or zinc salts, hydrogen peroxide or systems that generate hydrogen peroxide, (bi)carbonates or systems that generate (bi)carbonate, basifying agents other than the (bi)carbonate, and salts comprising titanium salts and scandium salts. Dyeing keratin fibers, preferably human keratin fibers such as the hair, comprises: treating the fibers with one or more cosmetic compositions containing, taken together or separately in the composition, ingredients comprising (a) one or more ortho-diphenol derivatives, (b) one or more manganese salts or zinc salts, (c) hydrogen peroxide or one or more systems that generate hydrogen peroxide, (d) one or more (bi)carbonates or one or more systems that generate (bi)carbonate, (e) one or more basifying agents other than the (bi)carbonate, and (f) one or more salts comprising titanium salts and scandium salts, where the pH of at least one of the compositions comprising the ingredients (a)-(f) is alkaline, which is greater than 7, and the composition comprising (f) is applied to the keratin fibers as the last step of the dyeing process. Independent claims are included for: (1) cosmetic composition, containing compounds (a)-(f); and (2) a multi-compartment device comprising 2-6 compartments containing 2-6 compositions, in which are distributed ingredients (a)-(f), where the compositions are aqueous or pulverulent, with at least one of these compositions being aqueous.La présente invention concerne un procédé de coloration des fibres kératiniques, en particulier des fibres kératiniques humaines telles que les cheveux, dans lequel lesdites fibres sont traitées par une ou plusieurs compositions cosmétiques contenant, pris ensemble ou séparément dans la ou lesdites compositions, les ingrédi