Magnetoelectric (ME) antiferromagnetic Cr2O3, being exchange coupled to a ferromagnetic multilayer (Pt/Co/Pt)n, n ≥ 1, is treated as a multiphase multiferroic material with sophisticated multifunctional properties. It is shown that the exchange bias (EB) of the ferromagnetic hysteresis loop cannot only be controlled by the magnetic freezing field, H fr, but additionally also by an external electric freezing field, E fr, via the ME effect of Cr2O3. Either a gradual shift or complete switching from −H EB to +H EB on the magnetic field axis are possible. Here the influence of E fr at constant H fr on both the coercive field, H c, and the antiferromagnetic domain wall susceptibility, Δχ, and on the temperature dependence of the ME controlled quantities H c(T) and H EB(T) is reported.