Dell founder Michael Dell has pushed for easier voting rules to help him win his battle to take the PC maker private, offering a token 10c more per share to sweeten his $24 billion bid.
The new proposal is for approval to be based on a majority of votes cast by unaffiliated shareholders.
This would give Michael Dell and Silver Lake Partners, his private equity backer, a leg up in the face of opposition from billionaire investor Carl Icahn and several other investors.
The bidders had fallen short of the previous bar to success majority support of all unaffiliated shareholders, sources familiar with the matter said last week.
The proposed voting change would stop shareholders who abstained from voting being counted against the deal.
"That's huge," said Larry Hamermesh, a corporate law professor at Widener University School of Law in Wilmington, Delaware.
"Adding the qualifier means shares that don’t show don’t count where previously they did."
Dell shares rose 1.8% to $13.11 in premarket trading on the news.
Dell postponed a shareholder vote for the second time to 2 August and said the new proposal would be considered by its special committee of independent Dell directors.
"This is our best and final proposal," the bidders said in a letter to Dell's board, as it raised its bid to $13.75 per share conditional on the change in voting rules.
Billionaire investor Carl Icahn, who has amassed an 8.7% stake in Dell, is leading a charge with major shareholder Southeastern Asset Management against the buyout with an offer of his own.
He and others say Michael Dell's deal undervalues the world's No 3 personal computer maker.
Mr Hamermesh said those who had abstained previously might have known that their holding would be counted as a "no" and they might now have an incentive to vote.
Dell stock closed at $12.88 on the Nasdaq yesterday.