The liquid phase of metal-organic frameworks (MOFs) is key for the preparation of melt-quenched bulk glasses as well as the shaping of these materials for various applications; however, only very few MOFs can be melted and transformed into stable glasses. Here, the solvothermal and mechanochemical preparation of a new series of functionalized derivatives of ZIF-4 (Zn(im)2, where im- = imidazolate and ZIF = zeolitic imidazolate framework) containing the cyano-functionalized imidazolate linkers CNim- (4-cynanoimidazolate) and dCNim- (4,5-dicyanoimidazolate) is reported. The strongly electron-withdrawing nature of the CN groups facilitates low-temperature melting of the materials (below 310 °C for some derivatives) and the formation of microporous ZIF glasses with remarkably low glass-transition temperatures (down to only about 250 °C) and strong resistance against recrystallization. Besides conventional ZIF-4, the CN-functionalized ZIFs are so far the only MOFs to show an exothermic framework collapse to a low-density liquid phase and a subsequent transition to a high-density liquid phase. By systematic adjustment of the fraction of cyano-functionalized linkers in the ZIFs, we derive fundamental insights into the thermodynamics of the unique polyamorphic nature of these glass formers as well as further design rules for the porosity of the ZIF glasses and the viscosity of their corresponding liquids. The results provide new insights into the unusual phenomenon of liquid-liquid transitions as well as a guide for the chemical diversification of meltable MOFs, likely with implications beyond the archetypal ZIF glass formers.