  It is well known that Kasner-type cosmologies provide a useful framework for
analyzing the three-dimensional anisotropic expansion because of the
simplification of the anisotropic dynamics. In this paper relativistic
multi-fluid Kasner-type scenarios are studied. We first consider the general
case of a superposition of two ideal cosmic fluids, as well as the particular
cases of non-interacting and interacting ones, by introducing a
phenomenological coupling function $q(t)$. For two-fluid cosmological scenarios
there exist only cosmological scaling solutions, while for three-fluid
configurations there exist not only cosmological scaling ones, but also more
general solutions. In the case of triply interacting cosmic fluids we can have
energy transfer from two fluids to a third one, or energy transfer from one
cosmic fluid to the other two. It is shown that by requiring the positivity of
energy densities there always is a matter component which violates the dominant
energy condition in this kind of anisotropic cosmological scenarios.
