A range of modified amine- and anhydride-cured epoxy systems based upon diglycidyl ether of bisphenol A was produced, through the systematic incorporation of moieties termed functional network modifiers (FNMs) that serve to change the network structure in controlled ways. Here, the chosen FNM was trimethylolpropane triglycidyl ether (TTE). The resulting materials were characterized by Fourier transform infrared spectroscopy, thermal analysis, dielectric spectroscopy and measurements of direct current conduction. A progressive reduction in the glass transition temperature of the modified samples was seen with increasing TTE, which is interpreted in terms of changes in the network architecture of the resin. The molecular origins of the dielectric γ and β relaxation processes are proposed. The observed increase in conduction seen exclusively with increasing TTE content in the amine-cured systems is considered in terms of the chemistry of the FNMs, variations in free volume, changes in molecular dynamics and residual unreacted groups retained from the curing reaction. Specifically, we relate the observed increase in conduction to the presence of unreacted amine groups.