In the bidding competition for the Italian infrastructure group Atlantia, the Benetton family, together with the financial investor Blackstone, submitted an offer for around 12.7 billion euros.
They want to outdo the Spanish property developer Florentino Perez and his ACS group.
The offer provides for 23 euros per share, as the company announced on Thursday.
That's a premium of 24.4 percent to the closing price on April 5 before takeover rumors surfaced.
The Atlantia group, in which the Benetton family already holds around 33 percent, would be valued at around 12.7 billion euros.
The tug-of-war over Atlantia could also affect Germany's largest construction company, Hochtief - both Atlantia and ACS are involved.
Hochtief is also involved
Investors GIP and Brookfield, who specialize in infrastructure, said last week that they had presented a takeover bid for Atlantia to the Benetton family.
If Global Infrastructure Partners (GIP) and Canada's Brookfield prevail, it is agreed that Perez's construction group ACS will take over the majority of Atlantia's motorway toll concessions, which the company has in France, Spain and South America.
ACS and Atlantia have held the Spanish motorway operator Abertis together since 2017, and Hochtief also has a stake in it.
Perez is also known as the president of Real Madrid football club.
If one of the consortia prevails, Atlantia could disappear from the stock exchange.
In addition to toll roads, the Italian infrastructure group also owns airports in Rome and southern France.