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When properly designed, a dielectric multilayer can sustain Bloch surface waves (BSWs). Using a multiheterodyne scanning near-field optical microscope that resolves phase and polarization, we will show that a thin dielectric structure deposited on the multilayer deflects the BSW propagation according to Snell's law. Moreover, the mechanism involved in this process is a transfer of energy from the BSW state in the bare multilayer to the new BSW state generated by the presence of the thin dielectric structure. No relevant radiative counterpart occurs. This characteristic validates the treatment of BSWs at the surface of dielectric multilayers as a two-dimensional phenomenon.