  We present a new suite of cosmological zoom-in hydrodynamical ($\approx 20\,
\mathrm{pc}$ spatial resolution) simulations of Milky-Way mass galaxies to
study how a varying mass ratio for a Gaia-Sausage-Enceladus (GSE) progenitor
impacts the $z=0$ chemodynamics of halo stars. Using the genetic modification
approach, we create five cosmological histories for a Milky-Way-mass dark
matter halo ($M_{200} \approx 10^{12} \, M_\mathrm{\odot}$), incrementally
increasing the stellar mass ratio of a $z\approx2$ merger from 1:25 to 1:2,
while fixing the galaxy's final dynamical, stellar mass and large-scale
environment. We find markedly different morphologies at $z=0$ following this
change in early history, with a growing merger resulting in increasingly
compact and bulge-dominated galaxies. Despite this structural diversity, all
galaxies show a radially-biased population of inner halo stars like the
Milky-Way's GSE which, surprisingly, has a similar magnitude, age, $\rm [Fe/H]$
and $\rm [\alpha/Fe]$ distribution whether the $z\approx2$ merger is more minor
or major. This arises because a smaller ex-situ population at $z\approx2$ is
compensated by a larger population formed in an earlier merger-driven starburst
whose contribution to the GES can grow dynamically over time, with both
populations strongly overlapping in the $\rm [Fe/H]-\rm [\alpha/Fe]$ plane. Our
study demonstrates that multiple high-redshift histories can lead to similar
$z=0$ chemodynamical features in the halo, highlighting the need for additional
constraints to distinguish them, and the importance of considering the full
spectrum of progenitors when interpreting $z=0$ data to reconstruct our
Galaxy's past.
