The right to petition for action implicitly includes the right to petition against an action. As such, it should be possible to sign any petition either "For" or "Against."
Signatures "Against" a petition need not disqualify the petition from consideration, they merely register the weight of argument on each side of the issue.
The additional ability to add a brief (100 word?) signing statement to each petition signature would be even better, but could understandably be cumbersome.