A framework is presented for including second-order perturbative corrections to the radiation patterns of parton showers. The formalism allows to combine $O\left({\alpha }_s^2\right)$-corrected iterated $2\to 3$ kernels for “ordered” gluon emissions with tree-level $2\to 4$ kernels for “unordered” ones. The combined Sudakov evolution kernel is thus accurate to $O\left({\alpha }_s^2\right)$. As a first step towards a full-fledged implementation of these ideas, we develop an explicit implementation of $2\to 4$ shower branchings in this letter.