When an intense light field strongly interacts with the band structure of a solid, the formation of hybrid light-matter quantum states becomes possible. Examples of such Floquet-Bloch states have been reported, but engineering of the band structure using Floquet states can suffer from dissipation and decoherence. Sustaining the necessary quantum coherence of the light-matter interactions requires robust electronic states in combination with strong fields of suitable polarization and frequency. Here, we explore the quantum coherent coupling of nano-focused surface plasmon polaritons (SPP) to distinct electronic states in the band structure of a solid. We observe above-threshold electron emission from the Au(111) Shockley surface state by the absorption of up to seven SPP quanta. Using time-resolved photoelectron spectroscopy the coherence of the interaction of the SPPs with the surface state during electron emission is investigated and the process is shown to be similar to light-driven above threshold electron emission. Ultimately, our work could render SPP-based Floquet engineering in nano-optical systems feasible.