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Recent studies based on numerical models of the Local Group predict the existence of field haloes and galaxies that have visited both the Milky Way and M31 in the past, called Hermeian haloes. We extend this analysis beyond the Local Group using two high-resolution dark matter-only N-body simulations from the MultiDark suite. We define Hermeian haloes as field haloes which had close interactions with two other more massive field haloes in the past, called targets. We find that Hermeian haloes are a more extreme example of field haloes with interactions in the past than the well-known backsplash haloes that experienced only one interaction. Compared to backsplashers, Hermeians have more concentrated density profiles and tend to occupy more overdense regions. They also have higher velocities relative to their target haloes and relative to their neighbours within 1~$h^{-1}\; \mathrm{Mpc}$. Hermeian haloes can be found around every halo in the simulation (if the resolution is sufficient) and make up 0.4 to 2.3 per cent of the total number of field haloes (for haloes more massive than $10^{10}\; h^{-1}\;\mathrm{M_{\odot}}$ and $3.3 \times 10^{7}\; h^{-1}\;\mathrm{M_{\odot}}$, respectively), increasing to 10 per cent in overdense regions. They tend to be distributed close to the line connecting their targets, which may help to identify Hermeian haloes in observations. We also identify Local Group analogues in the simulation and find that about one-third (15 out of 49) of them contain Hermeian haloes if the distance between the two main haloes is below 1~$h^{-1} \;\mathrm{Mpc}$.