New York-based Coty last month went public with a $10 billion, or $23.25 per share, cash offer for Avon, only to have the target reject the overture and say it has no interest in discussing the transaction. Avon, which has been dealing with foreign bribery charges, increased competition and narrowing profit margins, on April 9 hired a new CEO and said it intends to go it alone.

Privately held Coty, a fragrance maker controlled by German family holding company Joh. A. Benckiser GmbH, has said it has no desire to go hostile on Avon. But late Wednesday it moved a step closer to that strategy when it returned with a sweetened $24.75 per share offer backed by equity financing from Berkshire and existing shareholders and debt provided by J.P. Morgan Chase & Co. The suitor again called on Avon to open talks about a potential deal.

Coty in a letter to Avon management said that since making the initial offer last month "we have spent significant time listening to your shareholders and analyzing public information," adding that "we continue to believe that our proposal would provide compelling value to Avon's shareholders relative to a difficult and uncertain multi-year turnaround on a stand-alone basis."

Avon of New York in a statement disclosing the receipt of the letter said its board would consider it "in due course."

In presenting a revised bid, Coty appears to be hoping Avon shareholders will pressure the company to engage in negotiations. Certainly Avon's most recent financial statement did not boost investor confidence.

On May 1, Avon reported first-quarter earnings of $26.5 million, or 6 cents a share, on sales of $2.58 billion, compared to a $143.6 million profit on revenue of $2.63 billion a year prior.

Excluding certain items, the company earned 10 cents per share for the quarter, well below the 28 cents per share analyst estimate.

In setting a May 14 deadline for Avon to open discussions, Coty said again it would walk away should Avon not come to the table. "We will have to inform the public markets of the circumstances of our withdrawal," Coty warned.

The suitor said that should the two sides engage in talks but fail to come to terms acceptable to both sides, "we will simply indicate so in a mutually agreeable statement and part company as friends."

Avon shareholders might soon have other options to consider. According to reports, private equity firm Richmont Holdings Inc. has retained advisers and is arranging financing to make its own bid for the cosmetics company.