I cannot speak for all jurisdictions, but for the jurisdiction where I practice divorce law the answer is “yes”. See Utah Code § 30-3-4(2)(b):
(b) If the court finds that there are substantial interests favoring restricting access that clearly outweigh the interests favoring access, the court may classify the file, or any part thereof other than the final order, judgment, or decree, as private. An order classifying part of the file as private does not apply to subsequent filings.
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