  We present recent progress in our calculation of $B_K$ with improved
staggered fermions using chiral extrapolations based on SU(3) staggered chiral
perturbation theory. We have accumulated significantly higher statistics on the
coarse, fine, and ultrafine MILC asqtad lattices. This leads to a reduction in
statistical error and an improved continuum extrapolation. Our updated result
is $\hat{B}_K = B_K(\text{RGI}) = 0.737 \pm 0.003(\text{stat}) \pm 0.046
(\text{sys})$. This is consistent with the result obtained using chiral
extrapolations based on SU(2) staggered chiral perturbation theory, although
the total error is somewhat larger with the SU(3) analysis.
