Hertz Global Holdings Inc. said a proposal from Knighthead Capital Management and Certares Management to buy the car renter out of bankruptcy was superior to an existing offer from a rival investor group.

The decision further escalates the brawl to own Hertz as travel rebounds and means the company’s current reorganization sponsor, a group led by Centerbridge Partners, would need to counter with an updated plan of their own to stay in the running to acquire the car renter.

If the company receives further proposals from either group that meet its qualifications, Hertz would hold an auction on May 10, according to a statement Wednesday. Centerbridge has until May 7 to submit a counteroffer which would kick off the auction process, the company said in the statement.

The Knighthead bid assigned Hertz an enterprise value of $6.2 billion, paid debt holders in full and offered shareholders cash and a chance to purchase warrants that valued their holdings at around $2.25 a share, Bloomberg previously reported.

Knighthead and Certares have been dueling with Centerbridge, Warburg Pincus and Dundon Capital Partners over ownership of Hertz, with both investor groups submitting multiple rounds of proposals to buy the company.

Hertz initially chose the Centerbridge plan, and U.S. Bankruptcy Judge Mary Walrath last month approved a so-called breakup fee for that group if it was later outbid. Any exit plan Hertz picks is subject to approval by Walrath in bankruptcy court.

Hertz has been rushing to exit bankruptcy by summer to take advantage of a hot stock market and to capture an expected increase in vacation rentals. The industry is raising prices as post-vaccination business and leisure travel surges and household-name rental companies don’t have enough cars for customers to drive off the lot.

The case is Hertz Corp. 20-11218, U.S. Bankruptcy Court, District of Delaware (Wilmington).