The emission of high-order harmonics from solids
\cite{ghimire11a,schubert14a,luu15a,golde08a} under intense laser-pulse
irradiation is revolutionizing our understanding of strong-field solid-light
interactions
\cite{ghimire11a,schubert14a,luu15a,vampa15b,yoshikawa17a,hafez18a,jurgens20a},
while simultaneously opening avenues towards novel, all-solid, coherent,
short-wavelength table-top sources with tailored emission profiles and
nanoscale light-field control\cite{franz19a,roscamCLEO21}. To date, broadband
spectra have been generated well into the extreme-ultraviolet (XUV)
\cite{luu15a,luu18b,han19a,uzan20a}, but the comparatively low conversion
efficiency still lags behind gas-based high-harmonic generation (HHG) sources
\cite{luu15a,luu18b}, and have hindered wider-spread applications. Here, we
overcome the low conversion efficiency by two-color wave mixing. A quantum
theory reveals that our experiments follow a novel generation mechanism where
the conventional interband and intraband nonlinear dynamics are boosted by
Floquet-Bloch dressed states, that make solid HHG in the XUV more efficient by
at least one order of magnitude. Emission intensity scalings that follow
perturbative optical wave mixing, combined with the angular separation of the
emitted frequencies, make our approach a decisive step for all-solid coherent
XUV sources and for studying light-engineered materials