[en] A tensor equations-of-motion formalism for the excitation of a many-body system is presented, following the same general approach as the uncoupled formalism presented in a previous article. It is designed to take explicit account of the geometrical constraints imposed on excitation operators by the requirements that stationary states should have good angular momentum and, for a charge-independent nuclear Hamiltonian, good isospin. These developments are particularly relevant for application to molecular, atomic, and nuclear systems. By recognizing the geometrical constraints and exploiting the invariance properties of the excitation operators, the equations of motion become more readily applicable to nonscalar systems; i.e. to systems with nonzero angular momentum and/or isospin