We propose, by performing advanced ab initio electron transport calculations, an all-oxide composite magnetic tunnel junction, within which both large tunneling magnetoresistance (TMR) and tunneling electroresistance (TER) effects can coexist. The TMR originates from the symmetry-driven spin filtering provided by an insulating BaTiO3 barrier to the electrons injected from the SrRuO3 electrodes. Following recent theoretical suggestions, the TER effect is achieved by intercalating a thin insulating layer, here SrTiO3, at one of the SrRuO3/BaTiO3 interfaces. As the complex band structure of SrTiO3 has the same symmetry as that of BaTiO3, the inclusion of such an intercalated layer does not negatively alter the TMR and in fact increases it. Crucially, the magnitude of the TER also scales with the thickness of the SrTiO3 layer. The SrTiO3 thickness becomes then a single control parameter for both the TMR and the TER effect. This protocol offers a practical way to the fabrication of four-state memory cells.