Magnetoelectric coupling at the interface between PbTi(Zr)O₃ (001)(PZT) and a Co film as well as its tuning by Zr substitutions is studied here from first principles. Chemically disordered 25 per cent Zr-doped compositions were modeled within the supercell approach. Our calculations suggest that ferroelectric ionic displacements in PZT can be locally enhanced, especially when the interfacial Ti cations are replaced with Zr. Regarding Co films their structure tends to become hexagonal for thicker films, while rather significant changes in Co magnetization are anticipated in response to the electric polarization reversal in PZT.