  In single-component theories of dark matter, the $2\to 2$ amplitudes for
dark-matter production, annihilation, and scattering can be related to each
other through various crossing symmetries. These crossing relations lie at the
heart of the celebrated complementarity which underpins different existing
dark-matter search techniques and strategies. In multi-component theories of
dark matter, by contrast, there can be many different dark-matter components
with differing masses. This then opens up a new, "diagonal" direction for
dark-matter complementarity: the possibility of dark-matter decay from heavier
to lighter dark-matter components. In this work, we discuss how this new
direction may be correlated with the others, and demonstrate that the enhanced
complementarity which emerges can be an important ingredient in probing and
constraining the parameter spaces of such models.
