  Observations of the Milky Way's stellar halo find that it is predominantly
comprised of a radially-biased population of stars, dubbed the Gaia
Sausage--Enceladus, or GSE. These stars are thought to be debris from dwarf
galaxy accretion early in the Milky Way's history. Though typically considered
to be from a single merger, it is possible that the GSE debris has multiple
sources. To investigate this possibility, we use the IllustrisTNG50 simulation
to identify stellar accretion histories in 98 Milky Way analogues -- the
largest sample for which such an identification has been performed -- and find
GSE-like debris in 32, with two-merger GSEs accounting for a third of these
cases. Distinguishing single-merger GSEs from two-merger GSEs is difficult in
common kinematic spaces, but differences are more evident through chemical
abundances and star formation histories. This is because single-merger GSEs are
typically accreted more recently than the galaxies in two-merger GSEs: the
median infall times (with 16th and 84th percentiles) are $5.9^{+3.3}_{-2.0}$
and $10.7^{+1.2}_{-3.7}$ Gyr ago for these scenarios, respectively. The
systematic shifts in abundances and ages which occur as a result suggest that
efforts in modeling these aspects of the stellar halo prove ever-important in
understanding its assembly.
