  We examine Simplified Models in which fermionic DM interacts with Standard
Model (SM) fermions via the exchange of an $s$-channel scalar mediator. The
single-mediator version of this model is not gauge invariant, and instead we
must consider models with two scalar mediators which mix and interfere. The
minimal gauge invariant scenario involves the mixing of a new singlet scalar
with the Standard Model Higgs boson, and is tightly constrained. We construct
two Higgs doublet model (2HDM) extensions of this scenario, where the singlet
mixes with the 2nd Higgs doublet. Compared with the one doublet model, this
provides greater freedom for the masses and mixing angle of the scalar
mediators, and their coupling to SM fermions. We outline constraints on these
models, and discuss Yukawa structures that allow enhanced couplings, yet keep
potentially dangerous flavour violating process under control. We examine the
direct detection phenomenology of these models, accounting for interference of
the scalar mediators, and interference of different quarks in the nucleus.
Regions of parameter space consistent with direct detection measurements are
determined.
