Herein, we present the production of either dimethyl ether (DME), methyl formate (MF) or dimethoxymethane (DMM), representing pivotal molecules for the green transformation of fuels and chemical industry, by the non-oxidative gas-phase conversion of methanol under the same reaction conditions. The product selectivity is optimized by tailoring the acidic and dehydrogenative sites of the bifunctional Cu/Hβ catalyst system by varying the SiO2/Al2O3 ratio of the Hβ zeolite (25 and 520) and the Cu loading (0.5 and 20 wt.%). At 240 °C, >99% (DME), 74.5% (MF), and 77.3% (DMM) selectivity is achieved with the respective catalysts 0.5%Cu/Hβ(25), 20%Cu/Hβ(520), and 0.5%Cu/Hβ(520). High acidic site concentration catalyzes DME formation, while the presence of Cu+ species is crucial for DMM formation, and Cu0 species mainly catalyze MF formation. A highly dynamic reaction behaviour is observed, when the dehydrogenative functionality is dominant (i.e., in the production of MF or DMM), presumably due to the dynamic nature of the Cu oxidation state, which is in turn influenced by possible by-products (H2 and H2O). While the catalytic activity in DME synthesis over 0.5%Cu/Hβ(25) is remarkably stable over 1500 min TOS, the activity in MF and DMM production over 0.5%Cu/Hβ(520) and 20%Cu/Hβ(520), respectively, can be successfully regenerated.