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The formation and decay of dark matter (DM) bound states deplete the thermal relic density during the chemical decoupling process, allowing for larger DM masses. While so far the bound state formation (BSF) has been described via the emission of an on-shell mediator, we point out that this particular process does not have to be the dominant one in general. If the mediator is coupled in a direct way to any relativistic species present in the early Universe, we demonstrate that BSF can much more efficiently occur through particle scattering. Consequently, DM can be heavier than previously expected. [ABSTRACT FROM AUTHOR]