Blackstone Group Inc on Friday secured the support of Bill Gates, Signature Aviation’s largest shareholder, stepping up its offer to buy the private jet services company in the face of a rival approach from Carlyle.

Blackstone’s deal with Gates’ Cascade Investment LLC for its $ 4.29 billion offer comes just hours after Signature confirmed Carlyle’s acquisition approach.

Blackstone and Cascade, which owns about a 20% stake in London-based Signature, are in advanced discussions with the company about their proposal which involves a cash offer of £ 3.81 per share, Blackstone said.

Shares in the company formerly known as BBA Aviation were down 5% to £ 4 on the FTSE 250 mid-cap index at 0804 GMT, yielding some of their 65% gain in the three weeks since Signature Aviation confirmed talks with Blackstone.

Carlyle did not immediately respond to a request for comment from Reuters.

The £ 3.81-a-share offer is Blackstone’s sixth proposal, Signature Aviation revealed last month, when it also rejected another proposal from Global Infrastructure Partners.

Blackstone said the terms of its deal with Cascade also contained voting arrangements such that Cascade will vote against any competitive proposal after a firm offer is made to Blackstone.

Under UK acquisition rules, Blackstone and Cascade must announce a firm intention to bid or withdraw by January 14.