Three grades of poly(ethylene terephthalate) (PET) produced by different synthesis routes and with different molar masses were reactively extruded with two tetra‐functional chain extenders, i.e., pyromellitic dianhydride (PMDA) and tetraglycidyl diamino diphenyl methane (TGDDM). The preferred reactivity of the coupling agents led to different long‐chain branched (LCB) structures, which can be related to different hydroxyl and carboxyl end group concentrations of the PET grades investigated. The complex viscosity and the transient elongational viscosity increased by up to two decades. Both the activation energy of flow and the loss angle indicate long‐chain branching. A more quantitative assessment of the extent of strain hardening was achieved by application of the molecular stress function (MSF) model. The two material parameters of the model revealed different behaviors depending on the chain extender used. The initial molar mass of PET and the concentration of end groups, i.e., hydroxyl and carboxyl, determine the structure of the polymer molecules. PMDA proved to be an excellent coupling agent for industrial processing which induces reproducibly either a star‐like, comb‐like, or randomly branched structure depending on the concentration of coupling agent added and the hydroxyl concentration of the PET employed. TGDDM led to a hyperbranched structure. POLYM. ENG. SCI., 59:396–410, 2019. © 2018 Society of Plastics Engineers