An unhindered polyol is used to react with an epoxidized soyate to make epoxidized soyate diester in the presence of a catalyst. The unhindered polyol can be 1,3-propanediol or any polyol having four or more carbon atoms with no two adjacent carbon atoms having hydroxyl functionality. Preferably, a combination of catalysts is used to promote the transesterification reaction of the epoxidized soyate with the unhindered polyol to yield a high percentage of epoxidized soyate diester with epoxy functionality retained. The primary catalyst is a metallic hydroxide, and the secondary catalyst is a titanate. Bioderived epoxidized soyate diester plasticizers useful for thermoplastics and thermosets result.