Isocyanate-modified polyester-epoxide polymer (i-PEEP) compositions are disclosed. The i-PEEP compositions comprise a reaction product of a polyepoxide compound, a polyisocyanate, and a polyester polyol composition. The ratio of epoxy equivalents to hydroxyl equivalents is within the range of 0.2 to 2. The i-PEEP index as defined herein is within the range of 100 to 200. The i-PEEP composition has a Tg within the range of −30° C. to 35° C. Low- and elevated-temperature processes catalyzed by bases or Lewis acids for making the i-PEEP compositions are also disclosed. In a simple yet innovative approach, a new class of polymers useful for coatings, elastomers, adhesives, sealants, and other valuable products is assembled from readily available starting materials without reliance on the polyamines typically used to cure epoxy systems.