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The fact that several copies of a local quantum state - when processed together - can generate a nonlocal correlation, i.e. the superactivation of quantum nonlocality, is a well-known feature of quantum mechanics. Most of research results focused strongly on the bipartite scenario. In this paper we show that the activation of violation of Svetlichny inequality, reported for the first time in our previous paper, is not an exceptional phenomenon but holds for a broad class of quantum states as well for pure as for mixed, noisy ones. [ABSTRACT FROM AUTHOR]