Extending the technique presented in our earlier work, the correlation-function expression for the shear viscosity is evaluated up to the first-density correction for a classical system of particles interacting with pair and three-body forces of short range which may have attractive parts and may allow for bound states. The results contain new terms as a result of the existence of bound states, in addition to those obtained for the first-density correction to the shear viscosity for the case of purely repulsive forces. In particular, ${\ensuremath{\eta}}_{\mathrm{KU}}$, ${\ensuremath{\eta}}_{\mathrm{UK}}$, and ${\ensuremath{\eta}}_{\mathrm{UU}}$ involve genuine three-body dynamics and give rise to finite contributions to the first-density correction. Diagrams are provided which help to visualize the various processes contributing to the shear viscosity. Finally, higher order density corrections and unstable clusters are briefly discussed.