Advances in theory are needed to match recent progress in measurements of coupled semiconductor resonators supporting terahertz plasmons. Here, we present a field-based model of plasmonic resonators that comprise gated and ungated two-dimensional electron systems. The model is compared to experimental measurements of a representative system, in which the interaction between the gated and ungated modes leads to a rich spectrum of hybridized resonances. A theoretical framework is thus established for the analysis and design of gated low-dimensional systems used as plasmonic resonators, underlining their potential application in the manipulation of terahertz frequency range signals.