Commercial edible vegetable oils in which part of their triglycerides are substituted with 1,3-diglycerides are healthier for human consumption than the original oils. This is because the human metabolism of 1,3-diglycerides is believed to occur through a distinct pathway with less probability of being deposited as fat in the body tissues. To obtain these enriched oils, conversion of triglycerides into diglycerides is carried out by glycerolysis using commercial crude glycerol containing dissolved alkali cations that homogeneously catalyze the reaction. The addition of a food production-compatible MgO as a supplementary solid basic catalyst, shortens the reaction time by half due to a combination of homogeneous and heterogeneous catalysis processes. In either homogeneously or homogeneousheterogeneously catalyzed glycerolysis, the increase of the reaction temperature in the range of 453-493 K increases the final 1,3-diglyceride content. Furthermore, in both glycerolysis processes the triglyceride content can be decreased in more than 60% with the consequent increase of total diglycerides to 50%, 70% of which are the 1,3-isomers. The glycerolysis reaction proceeds without altering the fatty acid distribution of the original oils.