There is a high interest in modifying the rheological properties of polyethylene terephthalate (PET) through structural modifications while maintaining its thermoplastic nature. This article reports real-time spectroscopic and rheological monitoring of the effects of reactive melt modification of PET with a multi-functional epoxide-triglycidyl isocyanurate (TGIC)-that lead to chain extension/branching and subsequently formation of gel-like structures. An infrared spectroscopic technique to monitor the simultaneously occurring degradation and chain extension/branching reactions was evaluated. The effects of reaction temperature, shear rate, and residence time were also investigated. Frequency scans at various time intervals on the reacting samples provided information on changes in the degree of branching and melt elasticity. The effect of method of sample preparation for chemorheological testing was also evaluated in this study. A 50% excess of the stoichiometric amount of TGIC for complete reaction with terminal carboxyl groups resulted in a self-similar polymeric structure of PET near the sol-gel transition point or a critical gel formation whose linear viscoelastic properties obey scaling law. An estimated fractal dimension from the experimental results was used to quantify the evolution of the branched network structure during the reactive melt modification.