At $2.6 billion, Staples' new offer is 14 percent higher than its previous bid.
Analysts say the new price will prove more enticing to Corporate Express shareholders than that company's proposed buyout of Lyreco SAS, which would then go head-to-head with the world's largest office products retailer.
"If you're smart, you take the money (from Staples) and run," said Anthony Chukumba, a U.S. securities analyst with FTN Midwest Securities, who put the chances of Corporate Express accepting the Staples bid as high as 85 percent.
In announcing May 21 that it would buy France's Lyreco on, Corporate Express argued that combination would offer better growth prospects than being snapped up by Staples. Corporate Express shareholders are due to vote June 18 on the proposed buyout of privately held Lyreco for around $2.7 billion in cash and shares, and discuss Staples' bid.
After Staples raised its bid Tuesday - a proposal that would require Corporate Express shareholders to reject the Lyreco deal - Corporate Express issued a statement saying it "will carefully review this increased offer."
Framingham, Mass.-based Staples has now offered 9.15 euros ($14.21) per share - or 1.67 billion euros in cash - up from earlier bids of 7.25 euros and 8 euros per share.
Corporate Express shares rose 6.8 percent to 8.93 euros ($13.88), and are now worth more than twice what they were when rumors of a Staples bid began circulating in early February.
Shares of Staples rose 61 cents, or 4.7 percent, to $13.73,, suggesting investors were not overly concerned that Staples would be overpaying.
"I think what Staples is trying to do is try to put some finality on this deal," said Dan Davidowitz, a portfolio manager with Polen Capital Management, which holds about $18 million worth of shares in Staples.
But he added the current Staples' offering price "is about as high as we'd like to see them go."
Under Dutch bidding rules, Staples cannot raise its offer again.
In bidding up Tuesday to a price that represents a 26 percent increase from its initial offer, Staples "knows it can afford to pay more, and they really want to do this deal. This makes too much strategic sense for Staples to walk away," said Chukumba.
Staples wants to acquire Corporate Express to bolster its more profitable segments serving business customers - including big businesses that are Corporate Express' mainstay in the U.S. and Europe - and overseas clientele.
Both rivals are trying to rebound from a slow U.S. economy that has hurt U.S. office products sales, and many analysts say a deal could benefit both companies by helping them cut costs.
In May, Staples pitched its second offer directly to shareholders, complaining that Corporate Express's management was unwilling to negotiate. Analysts saw Corporate Express' Lyreco deal as a maneuver to take advantage of its rising share price, triggered by Staples' offers, and thwart the American company.
On Tuesday, Staples lowered its threshold for acceptance by Corporate Express shareholders to 51 percent from 75 percent, and said a deal could close by early July.
Staples said three Corporate Express investors holding 23 percent of the company's shares have already agreed to its latest offer.
Should a deal with Staples go through and derail the Lyreco deal, Corporate Express could be obligated to pay a $47 million breakup fee to the French firm.
Analyst Fernand de Boer of Petercam Bank advised Corporate Express shareholders in a research note to sell their shares now because of a significant chance the Staples deal would fail, especially if management takes "poison pill" measures to thwart Staples, such as issuing new shares to delay the process.
