The problem of mining multidimensional inter-transactional association rules was recently introduced in [5, 4]. It extends the scope of mining association rules from traditional single-dimensional intratransactional associations to multidimensional inter-transactional associations. Inter-transactional association rules can represent not only the associations of items happening within transactions as traditional intratransactional association rules do, but also the associations of items among different transactions under a multidimensional context. “After McDonald and Burger King open branches, KFC will open a branch two months later and one mile away” is an example of such rules. In this paper, we extend the previous problem definition based on context expansions, and present a generalized multidimensional inter-transactional association rule framework. An algorithm for mining such generalized inter-transactional association rules is presented by extension of Apriori. We report our experiments on applying the algorithm to real-life data sets. Empirical evaluation shows that with the generalized intertransactional association rules, more comprehensive and interesting association relationships can be detected.