While the first kilometre-scale neutrino telescope, IceCube, is still under construction, alternative plans exist to build even larger detectors that will, however, be limited by a much higher neutrino energy threshold of 10 PeV or rather higher than 10 to 100 GeV. These future projects detect radio and acoustic pulses as well as air showers initiated by ultra-high-energy neutrinos. As an alternative, we here propose an expansion of IceCube, using the same strings, placed on a grid with a spacing of order 500 m. Unlike other proposals, the expanded detector uses methods that are understood and calibrated on atmospheric neutrinos. Atmospheric neutrinos represent the only background at the energies under consideration and are totally negligible. Also, the cost of such a detector is understood. We conclude that supplementing the 81 IceCube strings with a modest number of additional strings spaced at large distances can almost double the effective volume of the detector. Doubling the number of strings on a 800 m grid can deliver a detector that is a factor of 5 larger for horizontal muons at modest cost.