Various interacting lattice path models of polymer collapse in two dimensions demonstrate different critical behaviours, and this difference has been without a clear explanation. The collapse transition has been variously seen to be in the Duplantier–Saleur $\theta$-point university class (specific heat cusp), the interacting trail class (specific heat divergence) or even first-order. This talk will describe new studies that elucidate the role of three body interactions in the phase diagram of polymer collapse in two dimensions.