We have recently improved our model of active galactic nucleus (AGN) by attaching the supermassive black hole (SMBH) to a massive nuclear star cluster (NSC). Here we study the effects of this new model in massive, gas-rich galaxies with several simulations of different feedback recipes with the hydrodynamics code RAMSES. These simulations are compared to a reference simulation without any feedback, in which the cooling halo gas is quickly consumed in a burst of star formation. In the presence of strong supernovae (SN) feedback, we observe the formation of a galactic fountain that regulates star formation over a longer period, but without halting it. If only AGN feedback is considered, as soon as the SMBH reaches a critical mass, strong outflows of hot gas are launched and prevent the cooling halo gas from reaching the disk, thus efficiently halting star formation, leading to the so-called "quenching". If both feedback mechanisms act in tandem, we observe a non-linear coupling, in the sense that the dense gas in the supernovae-powered galactic fountain is propelled by the hot outflow powered by the AGN at much larger radii than without AGN. We argue that these particular outflows are able to unbind dense gas from the galactic halo, thanks to the combined effect of SN and AGN feedback. We speculate that this mechanism occurs at the end of the fast growing phase of SMBH, and is at the origin of the dense molecular outflows observed in many massive high-redshift galaxies.