  Models that connect galaxy and halo properties often summarize a halo's mass
accretion history (MAH) with a single value, and use this value as the basis
for predictions. However, a single-value summary fails to capture the
complexity of MAHs and information can be lost in the process. We present
MultiCAM, a generalization of traditional abundance matching frameworks, which
can simultaneously connect the full MAH of a halo with multiple halo and/or
galaxy properties. As a first case study, we apply MultiCAM to the problem of
connecting dark matter halo properties to their MAHs in the context of a dark
matter-only simulation. While some halo properties, such as concentration, are
more strongly correlated to the early-time mass growth of a halo, others, like
the virial ratio, have stronger correlations with late-time mass growth. This
highlights the necessity of considering the impact of the entire MAH on halo
properties. For most of the halo properties we consider, we find that MultiCAM
models that use the full MAH achieve higher accuracy than conditional abundance
matching models which use a single epoch. We also demonstrate an extension of
MultiCAM that captures the covariance between predicted halo properties. This
extension provides a baseline model for applications where the covariance
between predicted properties is important.
