Additive particles are generally infelicitous in out-of-the-blue contexts. Kripke (in Linguistic Inquiry 40(3):367–386, 2009) puts forward an influential idea that the additive presupposition they trigger has an anaphoric component that cannot be accommodated. Ruys (in Linguistic Inquiry 46(2):343–361, 2015) proposes an alternative analysis that the observation can be explained in terms of conditions on deaccenting, claiming that in light of exceptional cases where additive particles can be used felicitously out of the blue, it is better to analyse the additive presuppositions as existential presuppositions. However, such exceptional cases have not been given a systematic explanation so far. In this paper, we closely examine existing and novel examples where additive presuppositions are felicitously used out of the blue and argue that Ruys’s existential analysis as well as the Kripkean anaphoric approach face empirical issues. We propose a new analysis, according to which the sui generis infelicity of additive particles in out-of-the-blue contexts is due to their focus sensitivity. Specifically, when an additive particle is used, two interpretive processes take place: (i) identification of a contextually relevant set of focus alternatives, and (ii) evaluation of the additive presupposition based on the focus alternatives so identified, which may result in accommodation. We claim that the felicity conditions on out-of-the-blue uses of additive particles emerge from the interplay between (i) and (ii).