Background: Double charge exchange (DCE) nuclear reactions have recently attracted much interest as tools to provide experimentally driven information about nuclear matrix elements of interest in the context of neutrinoless double-$\beta$ decay. In this framework, a good description of the reaction mechanism and a complete knowledge of the initial and final-state interactions are mandatory. Presently, not enough is known about the details of the optical potentials and nuclear response to isospin operators for many of the projectile-target systems proposed for future DCE studies. Among these, the ${}^{20}\mathrm{Ne}+{}^{76}\mathrm{Ge}$ DCE reaction is particularly relevant due to its connection with ${}^{76}\mathrm{Ge}$ double-$\beta$ decay.