A hyperbranched poly(glycidol) has been synthesized and modified by acylation with 10-undecenoyl chloride to obtain hyperbranched polymers (HBPs) with different degree of modification. These HBPs have been used as reactive modifiers in a proportion of 3%, 5%, and 10% with respect to a biscicloaliphatic diepoxide cured using ytterbium triflate as thermal cationic initiator. The materials obtained have been characterized and their mechanical properties evaluated. Phase separated materials have been obtained, with a 2-fold increase in impact resistance without sacrificing thermomechanical properties, thermal stability or processability. This good combination of properties can be explained by the achievement of a regular microphase separation with a good interfacial interaction between the microparticles and the epoxy matrix. The compatibility between the HBP and the matrix can be tuned by changing the degree of modification, which leads to a variable amount of available hydroxyl groups of the HBP that can react with the epoxy groups. This chemical bonding occurs through the activated monomer mechanism (AM) which is typical of the cationic homopolymerization of epoxides