ABSTRACT A number of stellar open cluster (OC) pairs in the Milky Way occupy similar positions in the phase space (coordinates, parallax, and proper motions) and therefore may constitute physically interacting systems. The characterization of such objects based on observational data is a fundamental step towards a proper understanding of their physical status and to investigate cluster pair formation in the Galaxy. In this work, we employed the Gaia EDR3 data to investigate a set of 16 OCs distributed as 7 stellar aggregates. We determined structural parameters and applied a decontamination technique that allowed us to obtain unambiguous lists of member stars. The studied OCs span Galactocentric distances and ages in the ranges of $7\lesssim \, R_\mathrm{ G}(\textrm {kpc})\lesssim 11$ and $7.3\le \textrm {log}\, t\le 9.2$. Eight OCs were found to constitute four gravitationally bound pairs (NGC 5617–Trumpler 22, Collinder 394–NGC 6716, Ruprecht 100–Ruprecht 101, and NGC 659–NGC 663, the latter being a dynamically unevolved binary) and other four clusters constitute two interacting, but gravitationally unbound, pairs (King 16–Berkeley 4 and NGC 2383–NGC 2384, the latter being a dissolving OC). Other four OCs (Dias 1, Pismis 19, Czernik 20, and NGC 1857) seem not associated with any stellar aggregates. Apparently, clusters within bound and dynamically evolved pairs tend to present ratios of half-light to tidal radius larger than single clusters located at similar RG, suggesting that mutual tidal interactions may possibly affect their structural parameters. Unbound or dynamically unevolved systems seem to present less noticeable signature of tidal forces on their structure. Moreover, the core radius seems more importantly correlated with the clusters’ internal dynamical relaxation process.