Several large-scale components of the climate system may undergo a rapid transition as critical conditions are exceeded. These tipping elements are also dynamically coupled, allowing for a global domino effect under global warming. Here we focus on such cascading events involving the Greenland Ice Sheet (GIS), the West Antarctica Ice Sheet (WAIS) and the Atlantic Meridional Overturning Circulation (AMOC). Using a conceptual model, we study the combined tipping behavior due to three dominant feedbacks: the marine ice sheet instability for the WAIS, the height-surface mass balance feedback for the GIS and the salt-advection feedback for the AMOC. We show that, in a realistic parameter range of the model, a tipping of the WAIS can inhibit cascading events by preserving the AMOC stability.