Fano-ADC is a family of ab initio methods for the prediction of electronic decay widths in excited, singly and doubly ionized systems. It has been particularly successful in elucidating the geometry dependence of the inter-atomic decay widths in clusters and facilitated the prediction of new electronic decay phenomena. However, the available Fano-ADC schemes are limited to the second-order treatment of the initial state and the first-order treatment of the final states of the decay. This confines the applicability of the Fano-ADC approach to first-order decay processes, e.g., normal but not double Auger decay (DAD), and compromises the numerical accuracy of the schemes through the unbalanced treatment of electronic correlation. Here, we introduce the ADC(2,2) approximation for singly ionized states, which describes both initial and final states of the decay up to second order. We use the new scheme to construct the Fano-ADC(2,2) approximation for the decay widths and show that it provides superior accuracy for the decay widths of a series of processes. Moreover, the Fano-ADC(2,2) method provides access to second-order decay processes, such as DAD, which are qualitatively beyond the reach of the previously available Fano-ADC implementations.