Yes, you need only add 3 signature fields. The first person signs, saves, sends file to the second etc. You can try this yourself by creating a simple form and signing it yourself 3 times.
Can you do this in Acrobat Professional 7.x on the Mac? Whenever I do this and sign the signature fields, the previous signature fields go from a green checkmark to a green checkmark with a yellow warning triangle with an exclamation mark on it and only the final signature field is a green checkmark. Is this normal? Can I sign all three sections (some forms designed for manual pen-based filling-in require signatures all over the place) such that they all show green checkmarks instead?
FOUND THE SOLUTION TO MY OWN QUESTION: Okay, I just found the answer on on the Adobe website.In summary, the signature fields should be created throughout the document but not signed yet. Then you go back to the first signature field and "certify" the document rather than "sign" it and specify whether you only allow "form fields" to be filled in or allow that plus comments as well (you have a choice). Since the remaining signature fields are "form fields" (and you've already allowed form fields to be filled in during the "certification" process), all subsequent signature fields, when signed, will show up in the document as a pure green checkmark (without any yellow triangles with exclamation marks in them) with the first signature field showing up as a blue ribbon certificate when the document is next opened. This is particularly useful if the document is not an "Adobe form" but a paper form that somebody just scanned in and you use the Typewriter tool in Acrobat Pro to fill in the various fields.