  We study the possibility of a Dark Matter candidate having its origin in an
extended Higgs sector which, at least partially, is related to a new strongly
interacting sector. More concretely, we consider an i2HDM (i.e. a Type-I Two
Higgs Doublet Model supplemented with a Z_2 under which the non-standard scalar
doublet is odd) based on the gauge group SU(2)_1 x SU(2)_2 x U(1)_Y. We assume
that one of the scalar doublets and the standard fermion transform
non-trivially under SU(2)_1 while the second doublet transforms under SU(2)_2.
Our main hypothesis is that standard sector is weakly coupled while the gauge
interactions associated to the second group is characterized by a large
coupling constant. We explore the consequences of this construction for the
phenomenology of the Dark Matter candidate and we show that the presence of the
new vector resonance reduces the relic density saturation region, compared to
the usual i2DHM, in the high Dark Matter mass range. In the collider side, we
argue that the mono-Z production is the channel which offers the best chances
to manifest the presence of the new vector field. We study the departures from
the usual i2HDM predictions and show that the discovery of the heavy vector at
the LHC is challenging even in the mono-$Z$ channel since the typical cross
sections are of the order of 10^{-2} fb.
