  We calculate the kaon mixing B-parameters for operators arising generically
in theories of physics beyond the standard model. We use HYP-smeared improved
staggered fermions on the $N_f = 2+1$ MILC asqtad lattices. Operator matching
is done perturbatively at one-loop order. Chiral extrapolations are done using
"golden combinations" in which one-loop chiral logarithms are absent. For the
combined sea-quark mass and continuum extrapolation, we use three lattice
spacings: $a \approx 0.045, 0.06$ and $0.09 \text{fm}$. Our results have a
total error of 5-6%, which is dominated by the systematic error from matching
and continuum extrapolation. For two of the BSM $B$-parameters, we agree with
results obtained using domain-wall and twisted-mass dynamical fermions, but we
disagree by $(4-5)\sigma$ for the other two.
