Disclosed herein are methods for recovering diphosphonite-containing compounds from mixtures comprising organic mononitriles and organic dinitriles, using multistage countercurrent liquid-liquid extraction. Recovery is enhanced with one or more method steps. In a first step, a portion of the heavy phase from the settling section of the first stage is recycled to the settling section of the first stage. In a second step, a portion of the light phase from the settling section of the first stage is recycled to the mixing section of the first stage. In a third step, the first stage takes place in a mixer-settler, a Lewis base is introduced into the settling section of the first stage, and a complex of Lewis acid and Lewis base is formed in this settling section. In a fourth step, a polyamine is added to the first stage.