Given the growing constraints on WIMP dark matter, coannihilation scenarios gain more and more interest. However, in order to theoretically predict the relic density, different effects have to be taken into account. We introduce a so far neglected effect - Higgs enhancement - that significantly alters the prediction of the dark matter abundance. While the importance of long-range interactions mediated by vector bosons is established, the Higgs is usually thought to transmit contact interactions only. We show however that the Higgs can lead to similarly striking effects. Furthermore, we will demonstrate the significant effect of bound state formation via emission of gauge bosons in coannihilation scenarios featuring non-Abelian long-range interactions. While its impact was previously disregarded in literature, we will show examples in which without taking into account the radiative formation and decay of particle-antiparticle bound states the dark matter density prediction is off by up to 240% for dark matter heavier than 500 GeV. Finally, we demonstrate that the Higgs as long-rang force mediator alters similarly bound state formation and hence impacts the relic density prediction also via this process.