Apollo Management raised its offer for chemical company Huntsman by 2.8% to $6.5 billion Monday, widening the premium over rival suitor Basell.
The new offer, up 75 cents a share from Apollo's previous bid of $27.25 a share, was made through Apollo's Hexion unit.
Dutch-based Basell is also bidding to acquire Huntsman.
Huntsman declined to comment on the new bid, but a spokesman said the board of directors was in contact with both suitors and its advisors.
Basell, controlled by U.S. industrial group Access Industries, last month agreed to buy Huntsman for $25.25 for each of the 233 million Huntsman shares outstanding.
Access is "considering its options and will decide over the next few days whether to raise its offer," a spokesman for the company said.
Last week Hexiontopped Basell's offer, prompting Huntsman to say the Apollo bid was superior.
The Texas-based chemicals company said it had notified Basell that it could change its earlier recommendation that shareholders approve the Basell bid, but said it would take into account any changes in Basell's offer.
The move by Apollo - raising its already higher offer - may indicate that the company is trying to combat criticism of the first offer, one mergers and acquisition lawyer said.
"Clearly to bid against yourself that quickly after you made your first bid is unusual," said Morton Pierce, chairman of the mergers and acquisition group at law firm Dewey Ballantine in New York.
Pierce, who is not involved in the deal, said there could be some issue that has made the offer appear weaker or that Apollo has received feedback from a major shareholder that the bid was not high enough to offset support for the original offer.
A spokesman declined to comment on why Apollo raised its offer.
MatlinPatterson and the Huntsman family together own 57 percent of Huntsman's stock and had agreed to the Basell offer before Apollo made its bid.
If the Basell agreement with Huntsman is terminated, Apollo will pay $100 million of the $200 million termination fee, or 86 cents per share. Apollo has arranged financing. Basell was not immediately available to comment.
Huntsman shares gained 1% to trade at $28.29 on the New York Stock Exchange.
On Friday, those shares had closed at $28, moving above Hexion's earlier bid in anticipation that the deal would be sweetened.