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Adverbs functioning as degree modifiers are not the only devices used for positive scaling; cross-linguistically, another very common means of intensification is the prefixation. This paper is concerned with data of nine intensifying prefixes of Modern Greek ( arxi‑ ‘archi’, θeο‑ ‘god’, kata‑ ‘over’, pan‑ ‘all’, olo‑ ‘whole’, para‑ ‘over’, pend(a)‑ ‘five’, xilio‑ ‘thousand’, iper‑ ‘hyper’) that constitute a representative sample of Greek intensifying prefixes. The purpose of this paper is to account for prefix-base combinations, taking into consideration the semantic typology of gradable predicates of Kennedy & McNally (2005) and more precisely focusing on the question of how the open or closed scale on which the bases map their arguments relates to intensifying prefix-base combinations. Our aim is to arrive at a general conceptual framework that can analyze all cases of intensifying prefixes. The paper also aims to account for the polysemy found in intensifying prefixes.