The choice of organism to host a genetic circuit, the chassis, is often defaulted to model organisms due to their amenability. The chassis-design space has therefore remained underexplored as an engineering variable. In this work, we explored the design space of a genetic toggle switch through variations in nine ribosome binding site compositions and three host contexts, creating 27 circuit variants. Characterization of performance metrics in terms of toggle switch output and host growth dynamics unveils a spectrum of performance profiles from our circuit library. We find that changes in host context cause large shifts in overall performance, while modulating ribosome binding sites leads to more incremental changes. We find that a combined ribosome binding site and host context modulation approach can be used to fine-tune the properties of a toggle switch according to user-defined specifications, such as toward greater signaling strength, inducer sensitivity, or both. Other auxiliary properties, such as inducer tolerance, are also exclusively accessed through changes in the host context. We demonstrate here that exploration of the chassis-design space can offer significant value, reconceptualizing the chassis organism as an important part in the synthetic biologist's toolbox with important implications for the field of synthetic biology.