We perform a detailed study of multistable behaviour in an optically injected semiconductor laser modeled by single-mode three-dimensional rate equations. It turns out that there is a wealth of regions of bi- and multistability – associated with bifurcations of periodic orbits – in the plane of injection strength and injection detuning. We follow such bifurcations over a wide range of parameters, which reveals different mechanisms for multistability in the system. In this way, we find, among others, the coexistence of two different periodic orbits with a chaotic attractor. Our results open new possibilities for optical switching between several different outputs of the laser.