  The way in which mergers affect galaxy formation depends on both feedback
processes, and on the geometry and strength of the mergers themselves. We
introduce the PARADIGM project, where we study the response of a simulated
Milky-Way-mass galaxy forming in a cosmological setting to differing merger
histories, using genetically modified initial conditions. Each initial
condition is simulated with the VINTERGATAN and IllustrisTNG codes. While
VINTERGATAN has been developed with an emphasis on resolving the cold
interstellar medium, IllustrisTNG uses a subgrid two-phase model and
consequently scales to large volume simulations, making them ideal to examine
complementary views on how merger histories and feedback interact. Our genetic
modifications alter the mass ratio of an important $z \approx 2$ merger while
maintaining the halo's $z=0$ mass. Whether simulated with VINTERGATAN or
IllustrisTNG, smaller mass ratios for this early merger result in larger
galaxies at $z=0$, due to a greater build up of a kinematically cold disc. We
conclude that such broad trends are robustly reproducible; however, the
normalization of the resulting stellar sizes is substantially different in the
two codes (ranging between $0.5-1.7\ \rm{kpc}$ for VINTERGATAN but $1.3-7.0\
\rm{kpc}$ for IllustrisTNG). The VINTERGATAN galaxies systematically form stars
earlier, leading to a larger bulge component. Despite the difference in size
normalization, both simulation suites lie on the observed size-mass relation
for their respective morphological types. In light of these results, we discuss
the interplay between internal processes and large scale gravitational
interactions and gas accretion, and how the two galaxy models converge on
similar emergent trends but along different evolutionary pathways.
