Given the growing constraints on WIMP dark matter, coannihilation scenarios gain more and more interest. However, in order to theoretically predict the relic density accurately, different effects have to be taken into account. The most dominant include Sommerfeld enhancement and bound state formation. While the former is well established, we demonstrate that bound state formation via the emission of a gauge boson in dark matter models that feature non-Abelian long-range interactions can have significant impact on the prediction of the dark matter abundance. In relevant models, the Higgs boson can similarly act as long-range force mediator. While neglected in recent literature, we demonstrate its impact on the relic density both via Sommerfeld enhancement and bound state formation.