But she believes it is "very significant" that the government felt compelled to bring forward any amendments at all.
"The last time this happened was on the so-called Fair Elections Act," she told reporters at a press conference on Monday morning. "It's encouraging that public pressure is working.
"It's proof that, though they didn't listen to witnesses, they're watching the polls, and watching support for this bad bill slip away … under their feet."
When Prime Minister Stephen Harper decides any "product of PMO ...(is) less than 100 per cent perfection," she said, that's progress.
"But do those amendments satisfy my concerns that this is dangerous legislation? No."
That's why she and her lone caucus colleague, Bruce Hyer, intend to put forward five dozen amendments when the House of Commons public safety committee begins examining the bill clause-by-clause on Tuesday.
The proposed legislation would give the Canadian Security Intelligence Service more power to thwart suspected terrorist plots — not just gather information about them.
It would also allow CSIS to violate the Charter of Rights and Freedoms with a judge's permission, expand the sharing of federal security information, broaden no-fly list powers and create a new criminal offence of encouraging someone to carry out a terrorism attack.
Expanded spy powers 'most dangerous': May
In addition, the bill would make it easier for the RCMP to obtain a peace bond to restrict the movements of suspects and extend the amount of time they can be kept in preventative detention.
"Trying to fix this bill is mission impossible," May said before outlining her party's proposed changes.
"But it is important to make substantive, thoughtful amendments where possible."
To that end, she and Hyer will present the committee with amendments addressing a wide variety of concerns, from the "undue burden" the new provisions will put on the airline industry to requiring CSIS inform the RCMP of any planned covert actions.
In May's view, it is the section expanding the spy agency's powers that is "the most dangerous" aspect of the bill.
"The activities of the secret police will rarely connect themselves in a way that will allow them to go to court to be challenged there," she pointed out.
"Almost everything else in this bill is going to eventually end up before the courts, and go to the Supreme Court, and the bad parts will be judged unconstitutional," she predicted.
"But this section ... says to CSIS agents, you can go to a judge and get permission to violate the charter."
That, she said, is unheard of, which is why she's proposing CSIS should have to let the RCMP know what it has planned.
Despite the enhanced information-sharing provisions in the bill — which are also targeted for amendment by the Green duo — May pointed out that there is "no communication required" between law enforcement and departmental agencies.
Her proposal would at least ensure the RCMP is in the loop when CSIS is plotting out how to employ its new powers to disrupt potential threats.
Although neither May nor Hyer sit on the committee, they will be permitted to present — but not vote on — their amendments during clause-by-clause review Tuesday.
The NDP and Liberals have also called for changes to the legislation to protect civil liberties and improve oversight of security agencies.
But while May shares the other opposition parties' concerns over the lack of new oversight measures, she predicted any amendments to address that gap would be ruled out of order, as it would go beyond the scope of the bill.