The matrix pencil is a well known technique used to fit data as a sum of complex exponentials. The technique estimates the poles of the system, then solves a least squares problem for the amplitudes of the poles. This paper details an extension of the matrix pencil technique to match poles simultaneously to several data sequences which should have the same poles but may have differing amplitudes, some of which may be zero, associated with the poles. These sequences may arise from different excitations of a structure or from viewing scattering information from different directions.