  Recently a new Lagrangian framework was introduced to describe interactions
between scalar fields and relativistic perfect fluids. This allows two
consistent generalizations of coupled quintessence models: non-vanishing
pressures and a new type of derivative interaction. Here the implications of
these to the formation of cosmological large-scale structure are uncovered at
the linear order. The full perturbation equations in the two cases are derived
in a unified formalism and their Newtonian, quasi-static limit is studied
analytically. Requiring the absence of an effective sound speed for the coupled
dark matter fluid restricts the Lagrangian to be a linear function of the
matter number density. This still leaves new potentially viable classes of both
algebraically and derivatively interacting models wherein the coupling may
impact the background expansion dynamics and imprint signatures into the
large-scale structure.
