Try working "inside the box", so to speak.  Yes, its regretable that one can't play a chord and have the harmonizer yield a full chord.  Instead, try building a patch with two octaves (one +12, and one -12) and blend with the original.  I've made many "POG" type sounds with the PODHd500 that were very close to Joe Satriani's "Super Colossal".  Maybe add a little octoverb and you'll have a real thick sound.