"I am sorry, Mr. Aethelred, but you are neither the first one, nor would you be the last to think of compounding cores in a wand. I know this seems logical, and seems even plausible, but only a wandmaker can tell you the futility of that notion."
Seeing my confusion, he explained plainly, "There is a reason, I and many of my contemporaries advise our customers that it is the wand, that chooses a Wizard. The wands are simply so different, so vibrant and so distinguished, that no two wands could ever be the same."
Seeing me understand at least that, he continued, "That is why we feel and recognise the wands as sentient and conscious of their existence, just like we are. And therefore, if the wand is truly sentient, but not because of its wood, then it must be because of its core."
I interrupted, "Have you Mr. Ollivander, heard of the term holistic synergy?"
He nods, "Ah, yes! The idea that an entity is more than simply the sum of the individual and independent parts that are used to make it. There are many proponents of this theory for wands, just as there are many against it. As for the actual truth, there is simply no way for us to know either way."
He ends my line of question, but continues, where he was interrupted. "But what we do know, with absolute certainty, is that a core is what gives a wand, its personality. The nature of a wand, is depended on the core and where and from whom it was obtained. Each wand, even those from a same type of creature, is different, just as two unicorns are different and distinguished. But, they also have certain similarities."
He then picked up a wand before me and fiddled with it, unconsciously. "And that is why, wandmakers are aware, that an individual wand with two cores within them, reacts extremely violently. In the most minor cases, they explode, in the cases where two opposing and contrasting cores are used, they repel so violently, that they rival ten simultaneous artillery spells cast in a single spot. It is the balance of nature."
Seeing my defeated pose, he finished his explanation. "And that is why, people have tried all the imaginable ways to combine them. With opposing elements, personalities, nature, and sometimes even natural opposites like a Unicorn and Thestral, Horned Serpent and Thunderbird, and even other imaginable variants, but none succeeded."
Seeing me nod, and understand his point he ventured into a different line if thought.
"This kind of balance is also seen in normal wands. Two wands made of the same wood do not interact the same way, as two wands made of the same core, especially the wand core which was donated from the same animal. Not the same species mind you, the very same creature."
I nodded as I knew a bit of that. "Priori Incantatem. I heard of that. Two wands, even if made of different woods, but containing the same core obtained from the one creature, react when two wizards who hold those wands duel with one another, when they are in conflict to each other."
Garrick Ollivander looked shocked at that. "Fascinating, Mr. Aethelred. But I must ask, how did you come by this knowledge? It is quite an obscure bit of wandlore that has been spoken of in our circles, but never witnessed, and never observed."