High-order spherical microphone arrays offer many practical benefits including relatively fine spatial resolution in all directions and rotation invariant processing using eigenbeams. Spatial filtering can reduce interference from noise and reverberation but in even moderately reverberant environments the beam pattern fails to suppress reverberation to a level adequate for typical applications. In this paper we investigate the feasibility of applying dereverberation by considering multiple beamformer outputs as channels to be dereverberated. In one realisation we process directly in the spherical harmonic domain where the beampatterns are mutually orthogonal. In a second realisation, which is not limited to spherical microphone arrays, beams are pointed in the direction of dominant reflections. Simulations demonstrate that in both cases reverberation is significantly reduced and, in the best case, clarity index is improved by 15 dB.