We investigate the properties of mergers comparable to the Gaia-Sausage-Enceladus (GSE) using cosmological hydrodynamical simulations of Milky Way-like galaxies. The merger progenitors span an order of magnitude in their peak stellar mass ($3\times 10^8\lt M_{\star }/\rm {M}_{\odot }\lt 4\times 10^9$) and include both rotation and pressure-supported galaxies (0.10 < D/T < 0.77). In a minority of cases, the GSE-like debris is comprised of stars from more than one merger progenitor. However, there is a close similarity in their chemodynamical properties and the triaxial shapes of their debris, and so it is not always possible to distinguish them. The merger progenitors host a variety of luminous satellites (0 and 8 with $M_{\star }\gt 10^6\, \rm {M}_{\odot }$), but most of these do not follow the merger to low orbital energies. Between 0 and 1 of these satellites may survive to z = 0, but with no clear signatures of their past association. We show that the fraction of stars originating from GSE-like mergers is reduced for lower metallicities (reaching a minimum around [Fe/H] = -2), and also within 5 kpc of the Galactic Centre. Whilst these central regions are dominated by in-situ stars, the ex-situ fraction trends towards a 100 per cent asymptote when considering the most metal-poor stars ([Fe/H] ≪ -2.5). Considering this, its near proximity, and its small volume on the sky, the Galactic Centre lends itself as a prime environment in the search for the stars from the earliest galaxies, whilst avoiding contamination from GSE stars.