1) Since there is no location to reject a counter offer, not signing a CO#1 makes perfect sense, and
2) Since there is no location to reject a counter offer, you can sign CO#1 with "acceptance subject to" a subsequent rewritten CO#2.
Personally, if the entire CO is not acceptable I write "Buyers do not agree with counter offer." and then I initial it and send a second rewritten Counter Offer with my client's signature(s). The later is based on a conversation with one of the CAR lawyers I spoke with.