Process for dyeing keratin fibres, in particular human keratin fibres such as the hair, in which said fibres are treated, in one or more steps, with one or more cosmetic compositions containing the following ingredients, taken together or separately in said composition(s): a) one or more dyes chosen from oxidation dyes and direct synthetic dyes and dyes of natural origin; b) one or more Ti salts; optionally b1) one or more carboxylic acids of formula below: formula or a salt thereof, in which: - A represents a monovalent group when n has the value zero or a polyvalent group when n is greater than or equal to 1, saturated or unsaturated, cyclic or non-cyclic and aromatic or non-aromatic hydrocarbon-based group comprising from 1 to 50 carbon atoms which is optionally interrupted with one or more heteroatoms and/or optionally substituted, in particular with one or more hydroxyl groups; preferably, A represents a monovalent (C 1 -C 6)alkyl group or a polyvalent (C 1 -C 6)alkylene group optionally substituted with one or more hydroxyl groups; - n represents an integer between 0 and 10 inclusive; preferably, n is between 0 and 5, such as between 0 and 2; c) one or more non-cellulosic-based polysaccharides; preferably at least one of the compositions used in the dyeing process is at acidic pH, i.e. less than 7.0, preferably less than 5, in particular at a pH of between 0 and 4 inclusive, more particularly between 0.5 and 3.5, preferably between 1 and 3. a) one or more dyes chosen from oxidation dyes and direct synthetic dyes and dyes of natural origin; b) one or more Ti salts; optionally b1) one or more carboxylic acids of formula below: formula or a salt thereof, in which: - A represents a monovalent group when n has the value zero or a polyvalent group when n is greater than or equal to 1, saturated or unsaturated, cyclic or non-cyclic and aromatic or non-aromatic hydrocarbon-based group comprising from 1 to 50 carbon atoms which is optionally interrupted with one or more heteroatoms and/or optionally substituted, in particular with one or more hydroxyl groups; preferably, A represents a monovalent (C 1 -C 6)alkyl group or a polyvalent (C 1 -C 6)alkylene group optionally substituted with one or more hydroxyl groups; - n represents an integer between 0 and 10 inclusive; preferably, n is between 0 and 5, such as between 0 and 2; - A represents a monovalent group when n has the value zero or a polyvalent group when n is greater than or equal to 1, saturated or unsaturated, cyclic or non-cyclic and aromatic or non-aromatic hydrocarbon-based group comprising from 1 to 50 carbon atoms which is optionally interrupted with one or more heteroatoms and/or optionally substituted, in particular with one or more hydroxyl groups; preferably, A represents a monovalent (C 1 -C 6)alkyl group or a polyvalent (C 1 -C 6)alkylene group optionally substituted with one or more hydroxyl groups; - n represents an integer between 0 and 10 inclusive; preferably, n is between 0 and 5, such as between 0 and 2; c) one or more non-cellulosic-based polysaccharides; preferably at least one of the compositions used in the dyeing process is at acidic pH, i.e. less than 7.0, preferably less than 5, in particular at a pH of between 0 and 4 inclusive, more particularly between 0.5 and 3.5, preferably between 1 and 3.