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In this work we study this phenomenon in the multiple-copy regime, where many perfect copies of a given state can be produced and controlled. In this scenario the above definition leads to subtle intricacies as biseparable states can be GME-activatable, i.e. several copies of a biseparable state can display GME. We show that the set of GME-activatable states admits a simple characterization: a state is GME-activatable if and only if it is not partially separable across one bipartition of the parties. This leads to the second question of whether there is a general upper bound in the number of copies that needs to be considered in order to observe the activation of GME, which we answer in the negative. In particular, by providing an explicit construction, we prove that for any number of parties and any number <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>k<\/mml:mi><mml:mo>&amp;#x2208;<\/mml:mo><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mi mathvariant=\"double-struck\">N<\/mml:mi><\/mml:mrow><\/mml:math> there exist GME-activatable multipartite states of fixed (i.e. independent of <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>k<\/mml:mi><\/mml:math>) local dimensions such that <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>k<\/mml:mi><\/mml:math> copies of them remain biseparable.<\/jats:p>","DOI":"10.22331\/q-2022-06-13-735","type":"journal-article","created":{"date-parts":[[2022,6,13]],"date-time":"2022-06-13T15:10:03Z","timestamp":1655133003000},"page":"735","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":22,"title":["Genuine multipartite entanglement of quantum states in the multiple-copy scenario"],"prefix":"10.22331","volume":"6","author":[{"given":"Carlos","family":"Palazuelos","sequence":"first","affiliation":[{"name":"Departamento de An\u00e1lisis Matem\u00e1tico y Matem\u00e1tica Aplicada, Universidad Complutense de Madrid, E-28040 Madrid, Spain"},{"name":"Instituto de Ciencias Matem\u00e1ticas, E-28049 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Julio I. de","family":"Vicente","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Universidad Carlos III de Madrid, E-28911, Legan\u00e9s (Madrid), Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2022,6,13]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"V. 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