You can apply a security policy that prevents editing, via File -
Properties - Security.
We don't want to completely lock down the PDF until two different people apply their stamps to it. We want the first person to apply their stamps and then have a second person also apply their stamps to the document before it is locked down. However, we wanted to find a way to embed the first person's stamps in the document so they can't be deleted before moving onto the second person. Flattening the annotations makes it appear to be embedded in the document; however, the Advanced Editing tools still allow them to be deleted if the document is not locked through say a sign and certify procedure. If the Advanced Editing tools were disabled, this would solve the problem. I don't know if this is possible to do or not.
It's not. But if these are your employees who are doing it, instruct them not to. They work for you, don't they?