  In this paper we establish B\"{a}cklund transformations between solutions of
several cases of classical isotropic MHD and plasma equilibria and
corresponding anisotropic equilibria. The transformations appear to be
infinite-dimensional and allow building solutions with variety of physical
properties. We also present a new infinite-dimensional Lie group of intrinsic
symmetries of anisotropic plasma equilibria equations, similar to those for the
isotropic case.
