In recent years, 3-forms have been studied both in the context of late-time dark energy and primordial inflation since they can very naturally accommodate a near cosmological-constant behaviour. However, depending on the choice of the potential, the Universe can end up either in a Minkowski or a de Sitter state, or even being lead to a Little Sibling of the Big Rip (LSBR) event in the asymptotic future. The latter scenario leads to the eventual dissociation, at finite time, of initially bounded gravitational systems much like in the Big Rip case. We present a dynamical systems description that provides a global analysis of a cosmological model with a 3-form for any kind of potential, with/without dark matter. For the potentials that induce a phantom behaviour, we look for conditions to avoid the LSBR through an appropriate interaction between the 3-form and dark matter. Some implications at the level of linear perturbations are discussed.