  We examine theoretically how dipole-dipole interactions arising from multiple
photon scattering lead to a modified distribution of ground state populations
in a driven, ordered 1D array of multilevel atoms. Specifically, we devise a
level configuration in which a ground-state population accumulated due solely
to dipole-dipole interactions can be up to 20\% in regimes accessible to
current experiments with neutral atom arrays. For much larger systems, the
steady state can consist of an equal distribution of population across the
ground state manifold. Our results illustrate how dipole-dipole interactions
can be accentuated through interference, and regulated by the geometry of
ordered atom arrays. More generally, control techniques for multilevel atoms
that can be degraded by multiple scattering, such as optical pumping, will
benefit from an improved understanding and control of dipole-dipole
interactions available in ordered arrays.
