Mill Road Capital has officially increased its bid to acquire Cossette to $8.10 per share, beating competitor Cosmos Capital to the punch.

The increased bid values the Quebec City-based agency network at $135.3 million.

Cossette's board had previously approved an offer of $7.87 per share from Mill Road, the Greenwich, Conn.-based investment firm it contacted as part of a search of potential buyers.

However, Cosmos Capital, run by former Cossette executive François Duffar, matched that offer last week with an unsolicited bid, and suggested it might raise that bid as high as $8.10 if it got access to Cossette's private data.

Cossette rejected Cosmos' $7.87 offer, but the two companies were in discussions about Cosmos' financial ability to raise its bid.

Today's announcement from Cossette restates its rejection of Cosmos' matching bid, and recommends that shareholders withdraw any shares tendered to Cosmos' offer.

"We are pleased with the increased consideration under the Mill Road transaction" said Jean Lavigueur, chairman of the agency's special committee handling the sale process, in a release. "The board of directors and its special committee remain committed to maximizing value for shareholders while acting in the best interests of Cossette."

According to a story in Saturday's Globe and Mail, should Mill Road take control of the company, long-time chair Claude Lessard would keep his chairman title but relinquish day-to-day control to younger managers like Brett Marchand, currently head of the Toronto office, and Gregor Angus, who oversees operations in the U.K.

Shareholders are scheduled to meet Dec. 18 to consider and vote on Mill Road's offer.