Signals are coupled to and from stacked semiconductor dies through first and second sets of external terminals. The external terminals in the second set are connected to respective conductive paths extending through each of the dies. Signals are coupled to and from the first die through the first set of external terminals. Signals are also coupled to and from the second die through the conductive paths in the first die and the second set of external terminals. The external terminals in first and second sets of each of a plurality of pairs are connected to an electrical circuit through respective multiplexers. The multiplexers in each of the dies are controlled by respective control circuits that sense whether a die in the first set is active. The multiplexers connect the external terminals in either the first set or the second set depending on whether the bonding pad in the first set is active.