Set-up your signings to allow Counter Offers. This means instead of having to create a new signing for your clients every time a counter offer has been proposed, all you need to do is to create your initial Authentisign signing and check off Allow Counter Offers.
When you receive a counter offer, you can then go into the original signing, update the document to show the counter offer, set the locations for your client(s) initials for that counter offer, then send it out again for your clients to initial.
This way all the history of the signing will be in one signing session.
Please see the documentation here for written instructions.