Metal-organic frameworks that flex to undergo structural phase changes upon gas adsorption are promising materials for gas storage and separations, and achieving synthetic control over the pressure at which these changes occur is crucial to the design of such materials for specific applications. To this end, a new family of materials based on the flexible metal-organic framework Co(bdp) (bdp2- = 1,4-benzenedipyrazolate) has been prepared via the introduction of fluorine, deuterium, and methyl functional groups on the bdp2- ligand, namely, Co(F-bdp), Co(p-F2-bdp), Co(o-F2-bdp), Co(D4-bdp), and Co(p-Me2-bdp). These frameworks are isoreticular to the parent framework and exhibit similar structural flexibility, transitioning from a low-porosity, collapsed phase to high-porosity, expanded phases with increasing gas pressure. Powder X-ray diffraction studies reveal that fluorination of the aryl ring disrupts edge-to-face π-π interactions, which work to stabilize the collapsed phase at low gas pressures, while deuteration preserves these interactions and methylation strengthens them. In agreement with these observations, high-pressure CH4 adsorption isotherms show that the pressure of the CH4-induced framework expansion can be systematically controlled by ligand functionalization, as materials without edge-to-face interactions in the collapsed phase expand at lower CH4 pressures, while frameworks with strengthened edge-to-face interactions expand at higher pressures. Importantly, this work puts forth a general design strategy relevant to many other families of flexible metal-organic frameworks, which will be a powerful tool in optimizing these phase-change materials for industrial applications.