First of all, you posted in the Reader forum. I'll move your question to one of the Acrobat forums.
PDF files were not meant to be edited in such a way, although basic edits are possible with Acrobat.
What kind of "signature" are you referring to, exactly? If it's a Digital Signature then it's not possible. If it's an image then you can use the Edit Text & Images tool to do it, although it's not recommended.