  We study statistical models, specifically transfer matrices corresponding to
a multiparameter hierarchy of braid matrices of $(2n)^2\times(2n)^2$ dimensions
with $2n^2$ free parameters $(n=1,2,3,...)$. The simplest, $4\times 4$ case is
treated in detail. Powerful recursion relations are constructed giving the
dependence on the spectral parameter $\theta$ of the eigenvalues of the
transfer matrix explicitly at each level of coproduct sequence. A brief study
of higher dimensional cases ($n\geq 2$) is presented pointing out features of
particular interest. Spin chain Hamiltonians are also briefly presented for the
hierarchy. In a long final section basic results are recapitulated with
systematic analysis of their contents. Our eight vertex $4\times 4$ case is
compared to standard six vertex and eight vertex models.
