We present the results of a self-consistent $N$-body simulation following the evolution of a primordial population of thick disc globular clusters (GCs). We study how the internal properties of such clusters evolve under the action of mutual interactions, while they orbit a Milky Way-like galaxy. For the first time, through analytical and numerical considerations, we find that physical encounters between disc GCs are a crucial factor that contributed to the shape of the current properties of the Galactic GC system. Close passages or motion on similar orbits may indeed have a significant impact on the internal structure of clusters, producing multiple gravitationally bound sub-populations through the exchange of mass and even mergers. Our model produces two major mergers and a few small mass exchanges between pairs of GCs. Two of our GCs accrete stars from two companions, ending up with three internal sub-populations. We propose these early interactions and mergers between thick disc GCs with slightly different initial chemical compositions as a possible explanation for the presence of the spreads in metallicity observed in some of the massive Milky Ways GCs.
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