During their main-sequence lifetimes, the majority of all Galactic disc field stars must endure at least one stellar intruder passing within a few hundred au. Mounting observations of planet–star separations near or beyond this distance suggest that these close encounters may fundamentally shape currently observed orbital architectures and hence obscure primordial orbital features. We consider the commonly occurring fast close encounters of two single-planet systems in the Galactic disc, and investigate the resulting change in the planetary eccentricity and semimajor axis. We derive explicit four-body analytical limits for these variations and present numerical cross-sections which can be applied to localized regions of the Galaxy. We find that each wide-orbit planet has a few per cent chance of escape and an eccentricity that will typically change by at least 0.1 due to these encounters. The orbital properties established at formation of millions of tight-orbit Milky Way exoplanets are likely to be disrupted.