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We measured the spin-orbit torques (SOTs), current-induced switching, and domain wall (DW) motion in synthetic ferrimagnets consisting of Co/Tb layers with differing stacking order grown on a Pt underlayer. We find that the SOTs, magnetic anisotropy, compensation temperature and SOT-induced switching are highly sensitive to the stacking order of Co and Tb and to the element in contact with Pt. Our study further shows that Tb is an efficient SOT generator when in contact with Co, such that its position in the stack can be adjusted to generate torques additive to those generated by Pt. With optimal stacking and layer thickness, the dampinglike SOT efficiency reaches up to 0.3, which is more than twice that expected from the Pt/Co bilayer. Moreover, the magnetization can be easily switched by the injection of pulses with current density of about 0.5-2*107A/cm2 despite the extremely high perpendicular magnetic anisotropy barrier (up to 7.8 T). Efficient switching is due to the combination of large SOTs and low saturation magnetization owing to the ferrimagnetic character of the multilayers. We observed current-driven DW motion in the absence of any external field, which is indicative of homochiral Néel-type DWs stabilized by the interfacial Dzyaloshinkii-Moriya interaction. These results show that the stacking order in transition metal/rare-earth synthetic ferrimagnets plays a major role in determining the magnetotransport properties relevant for spintronic applications.