We describe multidimensional extensions to a one-dimensional approach to tunneling splittings using a relaxed potential in the imaginary-frequency normal mode of the relevant saddle point (Wang, Y.; Bowman, J. M. J. Chem. Phys. 2008, 129, 121103). Tests of these extensions are given for H3O+ and NH3 where full dimensional tunneling splittings are available and for the vinyl radical using a new full-dimensional potential energy surface.