Given a positive integer-valued vector u = (u 1 , . . . , u m ) withWe introduce a combinatorial construction termed a parking function multi-shuffle to generic u-parking functions and obtain an explicit characterization of multiple parking coordinates. As an application, we derive various asymptotic probabilistic properties of a uniform u-parking function of length m when u i = cm + ib. The asymptotic scenario in the generic situation c > 0 is in sharp contrast with that of the special situation c = 0.