  We explore a scenario where Dark Matter (DM) couples to the Standard Model
mainly via a scalar mediator ${\cal S}$ that is odd under a $Z_2$ symmetry,
leading to interesting collider signatures. In fact, if linear interactions
with the mediator are absent the most important DM production mechanisms at
colliders could lead to final states with missing transverse energy (MET) in
association with at least two fermions, such as di-jet or di-electron
signatures. The framework we consider is model-independent, in a sense that it
is only based on symmetry and formulated in the (extended) DM Effective Field
Theory (eDMEFT) approach. Moreover, it allows to address the smallness of
first-generation fermion masses via suppressed $Z_2$ breaking effects. From a
di-jet +MET analysis at the LHC, we find rather loose bounds on the effective
${\cal S}$-${\cal S}$-DM-DM interactions, unless the mediator couples very
strongly to SM fermions, while a future $e^+ e^-$ collider, such as CLIC, could
deliver tighter constraints on the corresponding model parameters, given the
mediator is leptophilic. We finally highlight the parameter space that allows
to produce the observed DM density, including constraints from direct-detection
experiments.
