The U.S. Securities and Exchange Commission formally proposed a new rule on Tuesday that could make it harder for shareholders to submit proposals dealing with social issues like executive pay and climate change.

The rule, now open to public comment, would hike the re-submission thresholds for shareholder resolutions, or recommendations that ordinary retail investors can make to a company's board. The SEC voted 3-2 to officially propose the rule.

Two of the SEC's commissioners, Allison Herren Lee and Robert Jackson Jr., dissented on the rule's proposal, saying that they would limit accountability of corporate executives and suppress shareholder rights.

Under the current system, shareholder resolutions can be excluded from firms' annual proxy materials if the proposals do not garner support from at least 3% of shareholders within one year of the proposal. The thresholds then rise to 6% within two years, and then 10% within three years.

"The assumption that vote totals reflect the merits of proposals risks depriving investors and the Commission of information that has long produced crucial transparency on corporate governance matters," said Commissioner Robert Jackson Jr. in prepared remarks.

If eventually passed, the new re-submission thresholds would become 5% on the first submission, 15% on the second and 25% of shareholder support on the third.

Also, if a proposal after three attempts does reach support from 75% of shareholders within five years, a proposal must take a "time out," SEC Chairman Jay Clayton explained in opening remarks. Any resolution that gains 25% of shareholder support year over year can be re-submitted if it is "potentially on a path toward more meaningful shareholder support," Clayton continued.

Investors who own at least 1% or $2,000 worth of a company's stock for one year can file shareholder resolutions and add their input to various board decisions.The SEC also proposed changing that eligibility threshold to a more "tiered approach." A shareholder would be able to submit a proposal if they held $2,000 worth of a company's stock for three years, $15,000 worth of stock for two years or $25,000 worth of stock for one year, under the new proposed rule.

The shareholder must also be able to meet with a company to discuss a proposal, and only one person can submit a proposal at a time, the rule stipulates.

If the resolution meets all of the SEC's criteria, the company must include the resolution in its annual proxy vote materials for its annual shareholder meeting. Separately, the SEC also voted to propose a rule that would require proxy advisors to provide more disclosures on possible conflicts of interests in their advice to institutional investors. The rule would also allow companies to review proxy materials before they are sent to shareholders. That vote was also passed 3-2.