We study the Wheeler-DeWitt equation for the cases of first- and second-order perturbations around the $\mathcal{M}\mathcal{S}({T}^{d})$ minisuperspace, which is the Wheeler superspace of all flat and orthogonal tori in $d$ dimensions. To first order, the Wheeler-DeWitt equation is an infinite-dimensional globally hyperbolic massless Klein-Gordon equation. A definition of a Hilbert space in that region of superspace is straightforward, but the dynamics is trivial. To second order, the Wheeler-DeWitt equation is an infinite-dimensional globally hyperbolic Klein-Gordon equation, but with a mass-squared term which is time dependent. This time dependence ruins the possibility of a simple definition of a Hilbert space.