When applied to the electromagnetic scattering problem, the method of moments (MoM) results in a full matrix representation which requires a large amount of computational resources. To circumvent this problem, the numerical technique presented here works directly on the efficiency of the interpolation scheme used in the MoM, introducing an extrapolated version of Gordon's interpolation. This new method is applied to a generalized version of the volume surface integral equation to solve two-dimensional scattering problems. It is shown how it results in the decomposition of the problem into three simpler independent problems which can be performed either in sequence or in parallel. The performances of the method are confirmed by convergence tests, and the extrapolated MoM is illustrated on the case of the scattering by a microstrip structure.