MCDHU is correct.
The reason for the limitation is the electrical supply split. Cat III dual approaches require two independent electrical sources and thats why QRH 5.04 states an electrical supply split is required for CAT III dual. When configured with single engine and an APU generator, if a fault occurs in one electrical system the other bus ties to the failed side and provides power. Therefore they are not split. When both engines are operational on a CAT III B (dual) approach they remain split even following an electrical failure on one side.
One cautionary note: following an engine failure and an APU running, the System Display (SD) ELEC page appears to show the two sides split. This is just for representational purposes and if a failure occurred on one side the tie would connect the failed side to the remaining generator.
Does that help?