We revise the radiative corrections to double-Dalitz decays ($P\to\ell\bar{\ell}\ell'\bar{\ell}'$), completing the full next-to-leading order calculation in QED as compared to existing calculations. As a result, we find mild differences with respect to previous studies, that might be relevant for extracting information about the mesons transition form factors. The latter play an important role in determining the hadronic light-by-light contribution to the anomalous magnetic moment of the muon. Finally, we outline an ongoing extension of this work to the $e^+e^-\to e^+e^- P$ processes.