A combined approach that uses the vibrational configuration interaction (VCI) and semiclassical instanton theory was developed to study vibrational tunneling spectra of molecules with multiple wells in full dimensionality. The method can be applied to calculate low-lying vibrational states in the systems with an arbitrary number of minima, which are not necessarily equal in energy or shape. It was tested on a two-dimensional double-well model system and on malonaldehyde, and the calculations reproduced the exact quantum mechanical (QM) results with high accuracy. The method was subsequently applied to calculate the vibrational spectrum of the asymmetrically deuterated malonaldehyde with nondegenerate vibrational frequencies in the two wells. The spectrum is obtained at a cost of single-well VCI calculations used to calculate the local energies. The interactions between states of different wells are computed semiclassically using the instanton theory at a comparatively negligible computational cost. The method is particularly suited to systems in which the wells are separated by large potential barriers and tunneling splittings are small, for example, in some water clusters, when the exact QM methods come at a prohibitive computational cost.