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Interesting question. Here's what I think.
I would assume that any matter inside an event horizon is already lost to the Black Hole. Thus, there would be no "normal" matter in the intersection of the event horizons. In fact, the combined event horizons would be distorted at the contact face, initially perhaps the shape of a dumbbell. I would also assume that with the event horizons already merging, it would be impossible for the black holes to separate i.e. they would merge into a black hole with a larger event horizon.
Someone else might have a different take on the scenario.
Regards, Rob
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