  In this paper we discuss representations of the Birman-Wenzl-Murakami algebra
as well as of its dilute extension containing several free parameters. These
representations are based on superalgebras and their baxterizations permit us
to derive novel trigonometric solutions of the graded Yang-Baxter equation. In
this way we obtain the multiparametric $R$-matrices associated to the
$U_q[sl(r|2m)^{(2)}]$, $U_q[osp(r|2m)^{(1)}]$ and $U_q[osp(r=2n|2m)^{(2)}]$
quantum symmetries. Two other families of multiparametric $R$-matrices not
predicted before within the context of quantum superalgebras are also
presented. The latter systems are indeed non-trivial generalizations of the
$U_q[D^{(2)}_{n+1}]$ vertex model when both distinct edge variables statistics
and extra free-parameters are admissible.
