We demonstrate engineering of the low-terahertz range plasmonic spectra of two-dimensional electron systems by modifying their geometry. Specifically, we have modelled, fabricated, and measured two devices for comparison. The first device has a rectangular channel, while the second is trapezoidal, designed to support a richer plasmonic spectrum by causing variation in the device width along the direction of plasmon propagation. We show that while plasmon resonant frequencies and field distributions in the rectangular device can largely be described by a simple one-dimensional analytical model, the field distributions modelled in the trapezoidal device shows a more complex pattern with significant variation along the length of the channel, so requiring a two-dimensional treatment. The results illustrate the potential of modifying the channel geometry to obtain different spectra in experiments, with potential applications in the design of novel terahertz-range devices, such as plasmon-based sources and detectors.