Uniform asymptotic high-frequency solution is developed for the diffraction of obliquely incident plane waves by a three-part impedance plane. The multiple interaction up to third order between the edges of the three-part impedance plane is obtained to yield a uniform scattered field. The employed formulations are based on a spectral iteration techique consisting of taking the Fourier integral representation of the n.tuply diffracted field by one junction as the incident field for the two-part plane where the (n+1)th diffraction will occur. Upon using the field components normal to the three-part surface, the (n+1)th diffracted field is obtained through the solution of a pair of uncoupled Wiener-Hopf equations. The contribution of the surface wave fields to the secondary as well as triply diffraction is included in the analysis.