In a superconducting spin switch consisting of ferromagnet-superconductor-ferromagnet (FSF) triple layers, the superconducting transition temperature ${T}_{c}$ can be controlled by switching the individual magnetization directions of the F layers from parallel (P) to antiparallel (AP) orientation. Here we study this effect on a Nb layer sandwiched between two ferromagnetic $\mathrm{Co}∕\mathrm{Pt}$ multilayers (ML) with perpendicular magnetic anisotropy. The coercive fields of the top and bottom ML are different so that a P or AP orientation of the F magnetizations can be easily achieved. ${T}_{c}$ is considerably higher in the P configuration when compared to the AP configuration. By comparison with a sample, where an insulating oxide layer is introduced between F and S on both sides of the S layer we confirm that the ${T}_{c}$ difference is due to the proximity effect. FSF triple layers with out-of-plane anisotropy may have potential applications in ultrahigh-density magnetic recording.