  We explore a generalization of nonrelativistic fermionic statistics that
interpolates between bosons and fermions, in which up to $K$ particles may
occupy a single-particle state. We show that it can be mapped exactly to $K$
flavors of fermions with imaginary polarization. In particular, for $K\!=\!2$,
we use such a mapping to derive the virial coefficients and relate them to
those of conventional spin-1/2 fermions in an exact fashion. We also use the
mapping to derive next-to-leading-order perturbative results for the pressure
equation of state. Our results indicate that the $K\!=\!2$ particles are more
strongly coupled than conventional spin-$1/2$ fermions, as measured by the
interaction effects on the virial expansion and on the pressure equation of
state. In the regime set by the unitary limit, the proposed $K\!=\!2$
deformation represents a universal many-body system whose properties remain
largely unknown. In particular, the system can be expected to become superfluid
at a critical temperature $T_c$ higher than that of the unitary limit. We
suggest it may be possible to realize this system experimentally by engineering
a polarized coupling to an electrostatic potential. Finally, we show that the
$K\!=\!2$ system does not display a sign problem for determinantal Monte Carlo
calculations, which indicates that $T_c$ can at least in principle be
calculated with conventional methods.
