Shear-coupled grain boundary (GB) migration is an effective plastic mechanism in absence of dislocation activity, ie. more favorably in nanocrystalline metals. For a given GB, several stress induced migration mechanisms, referred as coupling modes participate to the decrease of the elastic energy produced by the shear. They operate through the nucleation and motion of interfacial defects known as disconnections, carrying elementary shear strain characterized by their Burgers vector. However, so far, the coupling modes have been studied only under a simple shear, a situation much less complex than expected in a strained polycrystal, where multiple components of the stress tensor are present. Here we propose a more systematic investigation of the coupling modes when a composite shear is applied. This promotes the activation of new coupling modes. Using Molecular Dynamics simulations, we evidence these multiple coupling modes and the operation of their associate disconnections. Moreover, we also show that, even at low temperature, GB migration may occur by the successive occurrence of two modes: the relaxed shear appears then as an effective parameter, resulting from the combination of two operating elementary mechanisms.