Oh, regarding wands with common cores being used to work together, I rather imagine that, if both are casting the same spell, there could be a resonance between them that would actually increase the power of spell on it's target (don't laugh, resonance is a rather powerful force). I can see common core wands used against each other causing the priori incantem effect, but I'd think that will/intent has to come into play here, too.
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I wouldn't go as far as calling resonance powerful... cumulative, sure, but in of its self not powerful. I often said during my military career that the US Navy could be completely and utterly destroyed by the guy who invented the weapon that transmitted the resonate frequency of aluminum poprivets...
For some reason the idea of a pair of wands working in conjunction on a single spell, or linked in the sibling wand (hah!) effect would be a not good thing, not terribly unlike the reasons the Egon Spengler suggested the beams not be crossed... Which might be an interesting plotpoint all by it's self.