A reactive process is developed to extend the recycling of poly(ethylene terephthalate) (PET) into high-value applications, in particular into foam core sandwich structures. To achieve a cellular structure, a high extensional viscosity is required to prevent foam collapse during the final stabilisation phase of the extrusion process. This is obtained by reacting PET with tetrafunctional epoxy-based modifiers, which induce branching and a certain amount of crosslinking. The modification of the chemical architecture leads to a 50-fold increase in the apparent extensional viscosity. With these modified materials closed-cell foams are obtained using carbon dioxide as a foaming agent.