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The dependence on laser intensity of recently discovered plateau structures in laser-assisted x-ray–atom scattering, both with and without a static electric field present, is analyzed. Using the “three-step” model and the strong-field approximation we demonstrate a connection between laser-assisted, x-ray–atom scattering and high-order harmonic generation: For high laser-field intensities without a static field present, both processes have plateaus whose energies extend to the cutoff value 3.17Up, where Up is the ponderomotive potential energy. For x-ray–atom scattering in the presence of a static electric field we show that at high laser-field intensities two plateaus appear: One is our recently predicted high-energy plateau for the same process [Phys. Rev. Lett. 81, 5097 (1998)], while the other, low-energy plateau, has a differential cross section six orders of magnitude larger. The energy positions and relative magnitudes of these new plateaus are explained using semiclassical arguments.