Billionaire investor Carl Icahn sweetened his offer to acquire Pep Boys with a promise to top any bid from Bridgestone Corp. up to about $1.01 billion.

Icahn’s new offer includes a provision that would automatically beat any Bridgestone bid by 10 cents a share, up to a maximum of $18.10 a share, Philadelphia-based Pep Boys said Wednesday in a statement. Pep Boys’ board has determined that Icahn’s offer is superior, giving Bridgestone until 5 p.m. Thursday to respond with a new proposal.

The proposal will test whether Tokyo-based Bridgestone is willing to boost its offer beyond that threshold in order to expand deeper into the U.S. and create the world’s largest chain of tire and automotive centers. Icahn is looking to add Pep Boys’ 800 locations to the Auto Plus chain that he acquired earlier this year.

Traders in Pep Boys’ stock had been anticipating an offer higher than Icahn’s most recent bid of $16.50 a share, or about $918.7 million. Shares of the company, whose full name is Pep Boys — Manny, Moe & Jack, closed at $16.89 on Tuesday in New York. The stock gained 1.4 percent to $17.12 at 9:36 a.m. Wednesday.

The company, whose full name is Pep Boys — Manny, Moe & Jack, has about 7,500 service bays in addition to its retail business. Analysts have speculated Icahn still may be interested only in Pep Boys’ retail operation and would plan to sell the tire and services division to other interested parties like Bridgestone.