The multistep direct theory of Feshbach, Kerman and Koonin is applied to the analysis of nucleon inelastic scattering to the continuum. The one-step cross sections include contributions of incoherent particle-hole and collective excitations in the continuum. The multistep formalism is used with the non-DWBA matrix elements that involve the biorthogonally conjugated distorted waves. The multistep direct cross sections are combined with multistep compound and compound nucleus cross sections to give a complete analysis of proton inelastic scattering by iron at energies 29 MeV, 39 MeV and 62 MeV. The results show large contributions from the two-, three- and four-step reactions. A good agreement with experiment is obtained at all energies.