The design and implementation of Boolean logic functions in living cells has become a very active field within synthetic biology. By controlling networks of regulatory proteins, novel genetic circuits are engineered to generate predefined output responses. Although many current implementations focus solely on the genetic components of the circuit, the host context in which the circuit performs is crucial for its outcome. Here, we characterise 20 genetic NOT logic gates (inverters) in up to 7 bacterial-based contexts each, to finally generate 135 different functions. The contexts we focus on are particular combinations of four plasmid backbones and three hosts, two Escherichia coli and one Pseudomonas putida strains. Each NOT logic gate shows seven different logic behaviours, depending on the context. That is, gates can be reconfigured to fit response requirements by changing only contextual parameters. Computational analysis shows that this range of behaviours improves the compatibility between gates, because there are considerably more possibilities for combination than when considering a unique function per genetic construct. Finally, we address the issue of interoperability and portability by measuring, scoring, and comparing gate performance across contexts. Rather than being a limitation, we argue that the effect of the genetic background on synthetic constructs expand the scope of the functions that can be engineered in complex cellular environments, and advocate for considering context as a fundamental design parameter for synthetic biology.