A polystyrene-linked tris(triazolyl)methanecopper(I) cationic catalyst operates under heterogeneous conditions for the reaction of ethyl diazoacetate (EDA) with an array of substrates. Carbon–hydrogen as well as X–H (X = O, N) functionalization derived from the formal transfer of the carbene moiety (:CHCO2Et) from the copper center and subsequent insertion have been achieved, the reactions permitting repeated catalyst recycling and reuse. The addition of the same carbene unit to benzene leading to a cycloheptatriene derivative (Büchner reaction) or to phenylacetylene (cyclopropenation) took place at similar rates to the insertion processes and with the same catalyst recyclability. The use of this heterogenized cationic Cu catalyst in continuous flow has also been implemented. Key characteristics of the flow process are its high and constant turnover frequency (TOF) (residence times of 1 min still lead to full conversion in the reaction with ethanol after 48 h operation) and its suitability for the sequential performance of different types of carbene transfer reactions with a simple and affordable experimental setup.