The family of hybrid Prussian blue analogues includes many electroactive materials, where organic cations moving within the pores of the cyanide framework cause unusual and exploitable electrical properties. Our target material, (HIm)2K[Fe(CN)6], has a large dielectric constant in its two high-temperature phases due to the rotation of imidazolium ions in its cubic pores. The transition between these two phases affects the cation dynamics drastically, but itself depends on the unit cell parameter, varying from first-order to critical or even supercritical. We propose here to study this phase transition as a function of pressure. Mapping the phase space of this system will help to establish the link between its structure and the particular cation dynamics that correspond to desirable electrical properties.