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A weighted finite-state machine with n tapes (n-WFSM) defines a rational relation on n strings. The paper recalls important operations on these relations, and an algorithm for their auto-intersection. Through a series of practical applications, it investigates the augmented descriptive power of n-WFSMs, w.r.t. classical 1- and 2-WFSMs (weighted acceptors and transducers). Some of the presented applications are not feasible with the latter.