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Sudden stratospheric warming (SSW) events influence the Arctic Oscillation and midlatitude extreme weather. Previous work showed the Arctic stratosphere to be influenced by the Madden-Julian oscillation (MJO) and that the SSW frequency increases with an increase of the MJO amplitude, expected in a warmer climate. It is shown here that the zonal asymmetry in both the background state and forcing plays a dominant role, leading to either enhancement or suppression of SSW events by MJO-like forcing. When applying a circumglobal MJO-like forcing in a dry dynamic core model, the MJO-forced waves can change the general circulation in three ways that affect the total vertical Eliassen-Palm flux in the Arctic stratosphere. First, weakening the zonal asymmetry of the tropospheric midlatitude jet, and therefore preventing the MJO-forced waves from propagating past the jet. Second, weakening the jet amplitude, reducing the waves generated in the midlatitudes, especially stationary waves, and therefore the upward-propagating planetary waves. Third, reducing the Arctic lower-stratospheric refractory index, which prevents waves from upward propagation. These effects stabilize the Arctic vortex and lower the SSW frequency. The longitudinal range to which the MJO-like forcing is limited plays an important role as well, and the strongest SSW frequency increase is seen when the MJO is located where it is observed in current climate. The SSW suppression effects are active when the MJO-like forcing is placed at different longitudinal locations. This study suggests that future trends in both the MJO amplitude and its longitudinal extent are important for predicting the Arctic stratosphere response.