A process for making a block copolymer compatibilizer, comprising reacting an acrylic monomer that has functional groups with one or more vinyl monomers in the presence of a free radical initiator and a stable free radical to form a reaction product that includes residual unreacted acrylic monomer, and reacting one or more vinyl monomers with the reaction product to form a second block that incorporates the residual unreacted acrylic monomer. A blend composition comprising a first thermoplastic polymer, which has functional groups, a reactive block copolymer that has functional groups in two or more blocks, and a second thermoplastic polymer that is compatible with one block of the block copolymer, where the functional groups in the first thermoplastic react with the functional groups in the block copolymer.