Possible to save a password-protected interactive PDF with form-fields?

I have created an interactive (form-fields) PDF protected with encryption using two levels of password security.  The lesser password, the Document Open password, has permissions set to allow printing in high-res, and filling in form fields, and signing existing signature fields.

I would like to be able to send this PDF to someone, who knows the Document Open password, and have them complete the form fields and then be able to save the PDF to their hard drive, without removing its security, so that they can email it back to me as an attachment, or possibly upload it to my cloud folder, to which I've given them permissions.

When testing, I open the document as if I were the recipient, and type in the Document Open password. Although I can save the document, the form-fields data is erased. It saves only as a blank document.

Is there some additional level of Acrobat Pro that I need in order to have this capability? Or is it simply not available?

[Moved from the general Forum Lounge to a product-specific forum - Mod]