Data fragmentation has been proposed as a solution for protecting the confidentiality of sensitive associations when releasing data for publishing or external storage. To enrich the utility of data fragments, a recent approach has put forward the idea of complementing a pair of fragments with some (non precise, hence loose) information on the association between them. Starting from the observation that in presence of multiple fragments the publication of several independent associations between pairs of fragments can cause improper leakage of sensitive information, in this paper we extend loose associations to operate over an arbitrary number of fragments. We first illustrate how the publication of multiple loose associations between different pairs of fragments can potentially expose sensitive associations, and describe an approach for defining loose associations among an arbitrary set of fragments. We investigate how tuples in fragments can be grouped for producing loose associations so to increase the utility of queries executed over fragments. We then provide a heuristics for performing such a grouping and producing loose associations satisfying a given level of protection for sensitive associations, while achieving utility for queries over different fragments. We also illustrate the result of an extensive experimental effort over both synthetic and real datasets, which shows the efficiency and the enhanced utility provided by our proposal.