Current seismic imaging methods require data that is free of multiple reflections, which is why a range of multiple-removal algorithms have been developed. However, state-of-the-art algorithms for internal multiple removal are based on single event identification. They fail in the presence of finely layered (sub-wavelength) media which cause short-period internal multiple reflections, since these cannot be resolved individually. We present a method for seismic short-period internal multiple removal for 2D and 3D media as an extension of recent 1D work, based on the Marchenko theory. If we can separate the medium into a horizontally layered overburden and an arbitrary complex underburden we are able to remove the overburden-related effects of short-period (and long-period) internal multiples. We do not require an impedance model but achieve this with a smooth background velocity model, similar to what is used in other multiple removal algorithms. We give a 2D numerical example with a finely layered horizontal overburden and a laterally inhomogeneous underburden. Comparison of the image derived with our augmented Marchenko scheme with a conventional Marchenko image results in a considerable uplift. This is the first time that short-period internal multiples are removed correctly from 2D seismic data in a purely data-driven way.