While some observational studies have placed limits on the quantity and nature of accreted dwarf galaxies’ contributions to the Milky Way (MW) stellar halo (e.g., Unavane et al. 1996; Schlaufman et al. 2012), none has given a detailed account of their total relative contributions. In this study we test the prospects of using chemical abundances found in stars of the stellar halo to determine its formation history. To do this we utilize a statistical procedure called the expectation-maximization (EM) algorithm on ≥ 103−4 mock observations of the stellar chemical abundance ratio distributions (CARDs) found in the eleven simulated “MW-like” halos of Bullock & Johnston (2005) to recover the relative stellar mass contributions from representative accreted dwarf galaxies (templates). Using these templates we find that in most cases investigated we can recover luminosity fractions that sum over 90% of the total relative stellar mass contributions (from each progenitor template) to within a factor of 2. We also find that this method is particularly sensitive to older accretion events involving low-luminous dwarfs e.g. ultra-faint dwarfs --- or precisely those events that are too ancient to be seen by phase-space studies of stars and too faint to be seen by high-z studies of the early Universe. Since our results only exploit two dimensions in chemical abundance space (while near-future surveys promise to provide ~6-9+ important dimensions) we conclude that new high-resolution spectroscopic surveys of the stellar halo will allow us to recover the luminosity function of accreted dwarf galaxies --- and a detailed accretion history of the halo --- across cosmic time.