  In this paper we consider families of multiparametric $R$-matrices to make a
systematic study of the boundary Yang-Baxter equations in order to discuss the
corresponding families of multiparametric $K$-matrices. Our results are indeed
non-trivial generalization of the $K$-matrix solutions of the {\cal
{U}}_{q}[D_{n+1}^{(2)}] vertex model when distinct reflections and extra
free-parameters are admissible.
