A major challenge in three-dimensional (3D) bioprinting is the limited number of bioinks that fulfill the physicochemical requirements of printing while also providing a desirable environment for encapsulated cells. Here, we address this limitation by temporarily stabilizing bioinks with a complementary thermo-reversible gelatin network. This strategy enables the effective printing of biomaterials that would typically not meet printing requirements, with instrument parameters and structural output largely independent of the base biomaterial. This approach is demonstrated across a library of photocrosslinkable bioinks derived from natural and synthetic polymers, including gelatin, hyaluronic acid, chondroitin sulfate, dextran, alginate, chitosan, heparin, and poly(ethylene glycol). A range of complex and heterogeneous structures are printed, including soft hydrogel constructs supporting the 3D culture of astrocytes. This highly generalizable methodology expands the palette of available bioinks, allowing the biofabrication of constructs optimized to meet the biological requirements of cell culture and tissue engineering.