Shares of Elan Corp. PLC jumped Friday after Royalty Pharma once again raised its offer to buy the Irish drugmaker in an increasingly bitter takeover fight.

Royalty said it will now pay $13 in cash for each Elan share, and it will give stockholders the right to receive up to an additional $2.50 per share in milestone-based payments. That's up from a previous bid of $12.50 per share.

Elan had nearly 597 million shares outstanding at the end of March, so the latest offer totals about $7.76 billion, not counting the milestone-based payments.

Elan said its board will review the new offer, and its shareholders should take no action in the meantime.

Royalty, based in New York, is a privately held company that buys royalty interests in drugs and late-stage drug candidates. Friday's offer comes a day after it extended the closing date for its previous offer from June 6 to June 21.

Royalty made that offer, which amounts to about $7.5 billion, late last month. But Elan said the offer undervalued the company, and it went to court in both the United States and Ireland to secure orders temporarily halting Royalty.

Royalty said 7.5 percent of Elan shareholders had tendered their shares for that deal.

Elan has accused Royalty of deliberately misleading shareholders about the value of an agreement it made to sell its interest in the multiple sclerosis treatment Tysabri to former development partner Biogen Idec Inc. That deal is worth $3.25 billion in cash and recurring royalty payments.

Elan also recently announced a push to diversify its business through a string of acquisitions, and Royalty has made shareholder rejection of those deals a condition for completing its acquisition offer.

Royalty said Friday that if Elan shareholders approve these acquisitions, it will withdraw its offer and leave them "with an uncertain future overseen by a (board) with no track record of creating shareholder value."

Royalty initially offered to buy Elan in February for $11 per share. It said Friday it made its latest offer after receiving feedback from Elan shareholders, and the new deal gives them a stake in the "future upside of Tysabri." It includes additional payments if Tysabri receives Food and Drug Administration approval for an expanded use and if it hits some sales milestones.

"While Elan's board and management team appear to be solely focused on what we perceive to be increasingly desperate attempts to fend off Royalty Pharma's highly compelling offer, we have been carefully listening to shareholders and are pleased to revise our offer today based on their feedback," Royalty CEO Pablo Legorreta said in a statement from the company.

Royalty's latest offer also comes with the condition that more than 50 percent of shareholders need to accept the deal for Royalty to close it. That's a lower threshold than the 90 percent mark it had previously set. That also concerns Elan, which has said that the lower threshold could leave a large number of its shareholders with a minority stake in a Royalty-controlled company.

U.S.-traded shares of Elan rose 5.5 percent, or 70 cents, to $13.38 Friday afternoon, while the Standard & Poor's 500 index climbed less than 1 percent. The stock has climbed more than 30 percent since closing 2012 at $10.21.