Exactly what I want is to sing into a mike, play a 8-voice chord on a MIDI keyboard, and have my voice harmonized to those 8 notes by the Factory plugin.

Now, the Waves Morphoder claims to provide such a MIDI feature too, but this feature works only with certain DAWs, and my Ableton Live is not one of them. So I'm holding my fingers crossed that the Factory plugin will implement the feature correctly.