The combination of two or more reactive centers working in concert on a substrate to facilitate the reaction is now considered state of the art in catalysis, yet there still remains a tremendous challenge. Few heterogeneous systems of this sort have been exploited, as the active sites spatially separated within the rigid framework are usually difficult to cooperate. It is now shown that this roadblock can be surpassed. The underlying principle of the strategy presented here is the integration of catalytic components with excellent flexibility and porous heterogeneous catalysts, as demonstrated by the placement of linear ionic polymers in close proximity to surface Lewis acid active sites anchored on the walls of a covalent organic framework (COF). Using the cycloaddition of the epoxides and CO2 as a model reaction, dramatic activity improvements have been achieved for the composite catalysts in relation to the individual catalytic component. Furthermore, they also clearly outperform the benchmark catalytic systems formed by the combination of the molecular organocatalysts and heterogeneous Lewis acid catalysts, while affording additional recyclability. The extraordinary flexibility and enriched concentration of the catalytically active moieties on linear polymers facilitate the concerted catalysis, thus leading to superior catalytic performance. This work therefore uncovers an entirely new strategy for designing bifunctional catalysts with double-activation behavior and opens a new avenue in the design of multicapable systems that mimic biocatalysis.