  In the era of large-scale spectroscopic surveys in the Local Group (LG), we
can explore using chemical abundances of halo stars to study the star formation
and chemical enrichment histories of the dwarf galaxy progenitors of the Milky
Way (MW) and M31 stellar halos. In this paper, we investigate using the
Chemical Abundance Ratio Distributions (CARDs) of seven stellar halos from the
Latte suite of FIRE-2 simulations. We attempt to infer galaxies' assembly
histories by modelling the CARDs of the stellar halos of the Latte galaxies as
a linear combination of template CARDs from disrupted dwarfs, with different
stellar masses $M_{\star}$ and quenching times $t_{100}$. We present a method
for constructing these templates using present-day dwarf galaxies. For four of
the seven Latte halos studied in this work, we recover the mass spectrum of
accreted dwarfs to a precision of $<10\%$. For the fraction of mass accreted as
a function of $t_{100}$, we find residuals of $20-30\%$ for five of the seven
simulations. We discuss the failure modes of this method, which arise from the
diversity of star formation and chemical enrichment histories dwarf galaxies
can take. These failure cases can be robustly identified by the high model
residuals. Though the CARDs modeling method does not successfully infer the
assembly histories in these cases, the CARDs of these disrupted dwarfs contain
signatures of their unusual formation histories. Our results are promising for
using CARDs to learn more about the histories of the progenitors of the MW and
M31 stellar halos.
