We develop a four-body CDCC (continuum discretized coupled channel) model, aimed at describing reactions where both nuclei present a low breakup threshold. The only inputs are the interactions describing the colliding nuclei, and the four optical potentials between the fragments. The method is applied to the 11 Be + d and 7 Li + d systems. We show that, in general, breakup channels are crucial to reproduce the elastic cross sections. We suggest that the present wave functions could be used in future DWBA calculations.