  In previous work we studied the spin-boson model in the multiphoton regime,
using a rotation that provides a separation between terms that contribute most
of the level energies away from resonance, and terms responsible for the level
splittings at the anticrossing. Here, we consider a generalization of the
spin-boson model consisting of a three-level system coupled to an oscillator.
We construct a similar rotation and apply it to the more complicated model. We
find that the rotation provides a useful approximation to the energy levels in
the multiphoton region of the new problem. We find that good results can be
obtained for the level splittings at the anticrossings for resonances involving
the lower two levels in regions away from accidental or low-order resonances of
the upper two levels.
