Composites of polymers and graphene materials having enhanced electrical conductivity continue to attract intense research interest. Significant enhancement in electrical conductivity of such composites is limited by poor dispersion and distribution of the nanomaterial in the polymer, limiting the formation of a conductive filler-filler network at low percolation thresholds [1]. In this study, composites of PET and GNP at loadings up to 6 vol% were prepared by melt mixing in a twin-screw extruder and the role of ethylene methyl acrylate copolymer (EMA) in assisting dispersion of GNP within the PET matrix investigated. Inclusion of EMA improved GNP dispersion, reduced electrical and rheological percolation threshold values and, improved filler-filler (GNP-GNP) network formation. Rheological percolation thresholds were measured at 2.3 vol% and 1.1 vol% GNP in the absence and presence of EMA, respectively. Similarly, the electrical percolation threshold decreased from 1.7 vol% to 0.5 vol% GNP. The AC conductivity of PET changed from completely insulating behavior to semi-conductive with a value of 10^(-4) S/cm on inclusion of EMA. EMA facilitates the formation of a GNP-GNP network by increasing the melt strength due to a crosslinking reaction with PET. This reaction was confirmed from oscillatory rheology, FTIR and solid-state 13C NMR experiments. Reference [1] Y. Huang, C. Ellingford, C. Bowen, T. McNally, D. Wu, and C. Wan, “Tailoring the electrical and thermal conductivity of multi-component and multi-phase polymer composites,” Int. Mater. Rev., pp. 1–35, 2019.