A specimen-transport module adapted for use with each of a plurality of specimen-processing instruments of a multi-instrument clinical workcell. Such module is adapted to transport individual racks of specimen-containers relative to a specimen-aspiration probe of an associated instrument in a workcell, as well as to transfer selected racks of specimen-containers to an adjacent and identical specimen-transport module associated with another clinical instrument of the workcell. Since the same transport system is used to both present specimens for aspiration and to transfer specimens between instruments, there is no need for two independent conveyances as is characteristic of the prior art. Preferably, the specimen-transport module includes a magnetic X/Y transport system that operates beneath a rack-supporting surface to advance racks in mutually perpendicular directions across a supporting surface via magnetic forces.