  Portal Matter, with both SM and dark charges, induces KM between the $U(1)_D$
dark photon and the SM gauge fields offering an attractive mechanism by which
light thermal DM can obtain its observed relic density. If DM is fermionic, the
CMB informs us that it must be Majorana/pseudo-Dirac in nature to avoid
temperature-independent $s$-wave annihilation to SM states. How does this fit
into a more complete picture with the SM? A first step along this path may not
lie far away in energy due to the RGE running of the dark gauge coupling which
can becomes non-perturbative before the $\sim 10$'s of TeV range. This implies
that $U(1)_D$ must become embedded in a non-Abelian group, $G_D$, before this
occurs. The breaking of this group then produces the PM masses and the heavy
gauge fields associated with $G_D$ lead to new interactions between the SM and
the dark sector. In the past we have examined a set of distinctive
phenomenological features associated with this setup, based upon a number of
simplifying assumptions. It behooves us to explore the impact of these
assumptions on the predictions for possible experimental tests of these models.
In past analyses we assumed that DM is a VL, complex singlet under $G_D$. If
this assumption is relaxed, the dark sector must be augmented by additional
fermion(s) and the scalar fields needed to break the symmetries while
generating the needed Majorana-like mass terms for the DM. Here we analyze the
simplest extension of this kind wherein the DM lies in a VL doublet of $G_D$,
which we take to have the structure $SU(2)_I\times U(1)_{Y_I}$, leading to new
phenomenology. We find that given the current LHC search constraints on the
masses of heavy gauge bosons, the production of these new dark states with
large rates is unlikely at colliders unless they are produced singly in
$gg$-fusion or are resonantly enhanced.
