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Many languages across the world are known to have constructions that indicate pluractionality, entailing the existence of a multitude of events. In this paper, we introduce a pattern of pluractionality in sign language, via reduplication of verbal forms. We focus on the semantics of two pluractional markers that appear pervasively in French Sign Language (LSF): exact repetition (/‑rep/) and two‑handed alternating repetition (/‑alt/). We show that /‑rep/ and /‑alt/ fit into a larger typology of pluractionality in (spoken) language, where pluractional morphology specifies distribution over various dimensions. Additionally, however, the LSF pattern shows several novel properties. First, we observe a compositional puzzle, wherein the pluractional morphemes appear to be trivially redundant when they appear under distributive operators. Taking inspiration from work on ‘dependent indefinites’ in the nominal domain, we propose an analysis in which pluractional markers are scope‑taking predicates, that are licensed by distributive operators by taking scope over them. Second, we show that the rate of reduplication for both forms is iconically mapped to the rate of event repetition over time. We show that this iconic mapping is an at‑issue entailment that must be able to interact with logical meaning throughout the composition of a sentence. We propose an integrated model, in which pluractional morphemes incorporate an iconically defined predicate. In the context of our compositional system, this proposal makes the novel prediction of ‘scopable iconicity,’ in which the iconic meaning can be evaluated at different structural positions.