Yes, we can, if we are talking about one reason out of much larger group of reasons. We can also say: among other things, among other places, among other problems, among topics, etc.
I'm not sure if Andrew was actually wondering whether "among other reasons" could be enclosed by em dashes. If that was the question, the answer is also affirmative.
I've enclosed the phrase in em-dashes just before a "because" construction; is that OK?
With "among other reasons" placed there, it is possible to understand the sentence as saying that "our organization" was a reason formed among other reasons. If you don't want that as a possible reading, place the phrase at the end:
Our organization was formed because of that restructuring—among other reasons.
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