I agree with Nemsi (even if the LLC uses the owner's SSN), but in their telephone advice FinCEN personnel oftentimes say that if it is truly the same operation revoking the exemption and waiting 12 months is not necessary.
That's hearsay. Call them yourself and see what they tell you. If they say an amendment will suffice, document the phone call.
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In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.