  We study a renormalizable model of Dirac fermion dark matter (DM) that
communicates with the Standard Model (SM) through a pair of mediators -- one
scalar, one fermion -- in the representation $(\boldsymbol{6},\boldsymbol{1},
\tfrac{4}{3})$ of the SM gauge group $\text{SU}(3)_{\text{c}} \times
\text{SU}(2)_{\text{L}} \times \text{U}(1)_Y$. While such assignments preclude
direct coupling of the dark matter to the Standard Model at tree level, we
examine the many effective operators generated at one-loop order when the
mediators are heavy, and find that they are often phenomenologically relevant.
We reinterpret dijet and pair-produced resonance and $\text{jets} +
E_{\text{T}}^{\text{miss}}$ searches at the Large Hadron Collider (LHC) in
order to constrain the mediator sector, and we examine an array of DM
constraints ranging from the observed relic density $\Omega_{\chi}
h^2_{\text{Planck}}$ to indirect and direct searches for dark matter.
Tree-level annihilation, available for DM masses starting at the TeV scale, is
required in order to produce $\Omega_{\chi} h^2_{\text{Planck}}$ through
freeze-out, but loops -- led by the dimension-five DM magnetic dipole moment --
are nonetheless able to produce signals large enough to be constrained,
particularly by the XENON1T experiment. In some benchmarks, we find a fair
amount of parameter space left open by experiment and compatible with
freeze-out. In other scenarios, however, the open space is quite small,
suggesting a need for further model-building and/or non-standard cosmologies.
