You must save the document in order to apply the signature. That's how PDF signatures are designed. Acrobat does not keep track whether the next signature is being signed by the same signer or a different one.
I do not understand what you are trying to accomplish. Why a user needs to sign the same document several times? Does he make any changes to the document between signings? If he does then the next signature signs a different document than a previous one and the document's version without new changes may be useful. If he does not make any changes why does he need to sign again?
There is no equivalent in signatures of signing off a portion of a work.
I often see this sort of requirement from people starting out with digital signatures but it comes from a fundamental misunderstanding, a translation of paper-based workflows in an inappropriate way. A digital signature is ALWAYS applied to the whole document, not a region of it. Forget the stamp that signatures can put on a page: these are worthless and cause such confusion that they should be banned. Signatures are an invisible proof applied to a document, never anything smaller. Users should not be encouraged to sign a partial (uninspected) document, it leaves them open to action if there are things they have not reviewed.
[Why are stamps bad? Because they encourage people to look at the stamp and come to believe it has value. Because people believe the stamp has validity in a printed PDF. Because people believe the location of the stamp is significant. It is worthless because it can be faked in minutes by anyone with the slightest motivation and minimal skill. Every user working with sigital signatures must be properly trained to look at the actual signatures - off page - and validate their authority]
Signature appearance ("stamp" in Test Screen Name's language) in my opinion does have a value. When it is properly generated and applied it does convey information about the signer, time, location, reason, etc. If it weren't in the signature appearance, the document's reader would have to go to Signature Properties dialog to find all these bits of information, and some of them may not even be there if the signature appearance is highly customized. Test Screen Name is totally correct when saying that inexperienced digital signatures consumers may confuse the location of a signature appearance with the part of the document to which the signature allegedly applies.
PDF does allow the signers to sign portions of a document in a limited way. When the first signer signs a document, the signature covers the complete document. When document is modified and more content is added to it and the second signer signs the document, the second signature also covers the complete document but the first signature still covers only the part of the document before any modification was applied. In this case the signature appearance may be indicative of which part of the document this signature covers.
Actually, PDF specification provides for signatures covering only a part of the document (by controlling the /ByteRange entry). It is just that Acrobat (and AFAIK other PDF producers) do not have this functionality.