The ability to perform wide-range tuning of the magnetic field required to switch the magnetization of ferromagnetic layers with perpendicular magnetic anisotropy is of great importance for many applications. We show that, for (Au/Co)2(3) multilayers, this field can be changed from minus several kOe to plus several kOe because of changes to the coupling with a ferrimagnetic multilayer [either (Tb/Fe)6 or (Tb/Co)6] across a Au spacer (either homogeneous 1 nm thick or wedge-shaped). The adjustable parameters are the ratio of sublayer thicknesses of the ferrimagnet and the sequence of layers around the Au spacer. The change of the sequence from Co/Au/Co to Tb/Au/Co is accompanied by both the reduction of the interaction energy and the change of the magnetic field sign necessary to switch the magnetization of ferromagnetic multilayers. For a 1 nm thick Au spacer this fields change from positive (negative) to negative (positive) if the ferrimagnet is dominated by the transition metal (rare earth) as a result of its composition. The characteristic oscillatory behavior of RKKY-like coupling is demonstrated using a system with a wedge-shaped Au spacer.