In this study, we prepared a multi-layer Tb–Fe/Pt/Tb–Fe wire to develop a multi-level magnetic memory. By applying current, magnetizations of the Tb–Fe layers were inversion symmetrically switched by spin– orbit torque (SOT) generated from the middle Pt layer. Measurements of SOT showed that its efficiency had opposite polarities in the top and bottom Tb–Fe layers. The switching current density of the top and bottom Tb–Fe layers shifted in opposite directions under a uniform perpendicular magnetic field. Because the perpendicular magnetic field broke the inversion symmetry of SOT generated from the middle Pt layer, it could be used to control the switching current. Our results prove that the additional uniform and perpendicular magnetic field can enhance the controllability of the magnetization state in case of multi-level SOT-induced magnetization switching.