We present a scheme for cooling mechanical motion to the ground state in an optomechanical system. Unlike standard sideband cooling, this scheme applies to the so-called unresolved sideband regime, where the resonance frequency of the mechanical mode is much smaller than the cavity linewidth. Ground-state cooling becomes possible when assuming the presence of an additional, auxiliary mechanical mode and exploiting the effect of optomechanically induced transparency. We first consider a system where one optical cavity interacts with two mechanical modes and show that ground-state cooling of the unresolved mechanical mode is possible when the auxiliary mode is in the resolved sideband regime. We then present a modified setup involving two cavity modes, where both mechanical modes are allowed to be in the unresolved sideband regime.