We consider extensions of Fourier Neural Operators (FNOs) to advance their applicability in modeling complex physical dynamics. We address coupled and parameterized partial differential equations (PDEs), which arise ubiquitously in science and engineering, from multiphase flows and plasmas to climate dynamics and biological systems, yet remain relatively underexplored in learning-based frameworks. For coupled systems, we introduce and systematically investigate a design space of FNO architectures, identifying configurations that best capture interdependent physical processes. To handle parameterized dynamics, we propose a hypernetwork-based modulation approach that conditions the operator on input physical parameters, enabling flexible generalization across problem settings. We evaluate the proposed extensions on benchmark coupled PDEs with a particular focus on a one-dimensional capacitively coupled plasmas equation. The experiments show that our methods consistently outperform existing approaches, demonstrating the effectiveness of the coupled/parametric architectures.