  We investigate high-order harmonic generation in a solid, modeled as a
multi-level system dressed by a strong infrared laser field. We show that the
cutoff energies and the relative strengths of the multiple plateaus that emerge
in the harmonic spectrum can be understood both qualitatively and
quantitatively by considering a combination of adiabatic and diabatic processes
driven by the strong field. Such a model was recently used to interpret the
multiple plateaus exhibited in harmonic spectra generated by solid argon and
krypton [Ndabashimiye {\it et al.}, Nature 534, 520 (2016)]. We also show that
when the multi-level system originates from the Bloch state at the $\Gamma$
point of the band structure, the laser-dressed states are equivalent to the
Houston states [Krieger {\it el al.} Phys. Rev. B 33, 5494 (1986)] and will
therefore map out the band structure away from the $\Gamma$ point as the laser
field increases. This leads to a semi-classical three-step picture in momentum
space that describes the high-order harmonic generation process in a solid.
