The magnetic stability of a multilayer system formed by N slabs separated by nonmagnetic spacers has been studied, emphasizing the role of dipolar interactions among magnetic slabs. By means of numerical and analytical calculations, we have identified a regime in which the magnetic slabs behave independently, i.e., a critical thickness of the spacer at which dipolar interactions can be safely disregarded. The methodology used to establish this critical distance can be used for other geometries, as it is a useful tool to identify regimes of non-interacting magnetic slabs.