Data fragmentation has been proposed as a solution for protecting the confidentiality of sensitive associations when publishing data at external servers. To enrich the utility of the published fragments, a recent approach has put forward the idea of complementing them with loose associations, a sanitized form of the sensitive associations broken by fragmentation. The original proposal considers fragmentations composed of two fragments only, and supports the definition of a loose association between this pair of fragments. In this paper, we extend loose associations to multiple fragments. We first illustrate how the publication of multiple loose associations between pairs of fragments of a generic fragmentation can potentially expose sensitive associations. We then describe an approach for supporting the more general case of publishing a loose association among an arbitrary set of fragments.