The present disclosure relates to a composition for the oxidation dyeing of keratin fibers, for example human keratin fibers such as the hair, comprising: at least one fatty substance present in an amount greater than or equal to 20% by weight relative to the total weight of the composition; at least one oxidation base chosen from N,N-(β-hydroxyethyl)-para-phenylenediamines and the addition salts thereof with an acid, at least one dye precursor different than the at least one oxidation base chosen from N,N-(β-hydroxyethyl)-para-phenylenediamines and the addition salts thereof with an acid, at least one oxidizing agent, and optionally at least one alkaline agent. The disclosure also relates to a dyeing or lightening process using it. Another aspect of the disclosure is multi-compartment devices or kits for obtaining, after mixing together the compositions of the compartments, just before its application, a composition according to the disclosure.