  We extend the basic formalism of mimetic-metric-torsion gravity theory, in a
way that the mimetic scalar field can manifest itself geometrically as the
source of not only the trace mode of torsion, but also its axial (or,
pseudo-trace) mode. Specifically, we consider the mimetic field to be (i)
coupled explicitly to the well-known Holst extension of the Riemann-Cartan
action, and (ii) identified with the square of the associated Barbero-Immirzi
field, which is presumed to be a pseudo-scalar. The conformal symmetry
originally prevalent in the theory would still hold, as the associated Cartan
transformations do not affect the torsion pseudo-trace, and hence the Holst
term. Demanding the theory to preserve the spatial parity symmetry as well, we
focus on a geometric unification of the cosmological dark sector, and show that
a super-accelerating regime in the course of evolution of the universe is
always feasible. From the observational perspective, assuming the cosmological
evolution profile to be very close to that for $\L$CDM, we further show that
there could be a smooth crossing of the so-called phantom barrier at a low
red-shift, however for a very restricted parametric domain. The extent of the
super-acceleration have subsequently been ascertained by examining the
evolution of the relevant torsion parameters.
