  We consider an original variational approach for building new models of
quintessence interacting with dark or baryonic matter. The coupling is
introduced at the Lagrangian level using a variational formulation for
relativistic fluids, where the interacting term generally depends on both the
dynamical degrees of freedom of the theory and their spacetime derivatives.
After deriving the field equations from the action, we consider applications in
the context of cosmology. Two simple models are studied using dynamical system
techniques showing the interesting phenomenology arising in this framework. We
find that these models contain dark energy dominated late time attractors with
early time matter dominated epochs and also obtain a possible dynamical
crossing of the phantom barrier. The formulation and results presented here
complete and expand the analysis exposed in the first part of this work, where
only algebraic couplings, without spacetime derivatives, were considered.
