  There has been recent progress on computing the 4-rank of the tame kernel
$K_2(\mathcal{O}_F)$ for $F$ a quadratic number field. For certain quadratic
number fields, this progress has led to "density results'' concerning the
4-rank of tame kernels. These results were first mentioned in \cite{CH} and
proven in \cite{RO}. In this paper, we consider some additional quadratic
number fields and obtain further density results of 4-ranks of tame kernels.
Additionally, we give tables which might indicate densities in some generality.
