Little. There is not much that you can add that will make much difference. A solid additional barrier, like a drywall ceiling will help a lot. It will help a lot more if it is attached to isolation strips, but the typical suspended ceiling will help at least some. If you are dropping a solid ceiling, then using isolation strips and using two layers of drywall will make a big difference.
Don't forget to block all air to air transfer, like return air ducts.
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