We have studied the evolution of the Pt(111) Shockley-type surface state, which can be described as a surface resonance upon deposition of Ag monolayers. We have combined angle-resolved photoemission and scanning-tunneling-spectroscopy measurements with electronic-structure and photoemission calculations for true semi-infinite systems to guarantee a complete description of all surface-sensitive spectral features. An unusual energy shift and a considerable Rashba-type spin-orbit splitting of the surface resonance were observed and are discussed in terms of modifications in the electronic structure and relationship between the semi-infinite bulk and the surface potential via multiple electron scattering. The maximum magnitude of the splitting in momentum space amounts to 0.051 ± 0.007 °A−1 and appears as one of the highest values so far observed in the Gamma-type surface-state-resonance bands.