  In thermal dark matter models, allowing the dark matter candidate to
coannihilate with another particle can considerably loosen the relic density
constraints on the dark matter mass. In particular, introducing a single
strongly interacting coannihilation partner in a dark matter model can bring
the upper bound on the dark sector energy scale from a few TeV up to about 10
TeV. While these energies are outside the LHC reach, a large part of the
parameter space for such coannihilating models can be explored by future hadron
colliders. In this context, it is essential to determine whether the current
bounds on dark matter simplified models also hold in non-minimal scenarios. In
this paper, we study extended models that include multiple coannihilation
partners. We show that the relic density bounds on the dark matter mass in
these scenarios are stronger than for the minimal models in most of the
parameter space and that weakening these bounds requires sizable interactions
between the different species of coannihilation partners. Furthermore, we
discuss how these new interactions as well as the additional particles in the
models can lead to stronger collider bounds, notably in jets plus missing
transverse energy searches. This study serves as a vital ingredient towards the
determination of the highest possible energy scale for thermal dark matter
models.
