  We prove large-data scattering and existence of wave operators in the energy
space for the systems of $N$ defocusing fourth-order Schr\"odinger equations
with mass-supercritical and energy-subcritical power-type nonlinearity. In
addition, new nonlinear interaction Morawetz identities and inequalities are
given, suitable to shed lights on the decay of the solution with respect some
Lebesgue norms when the space dimensions are $d=3,4$.
