A trio of plaintiffs firms spent six years pressing claims over credit card swipe fees before reaching a record antitrust class action settlement on July 13, setting themselves up for a potentially enormous fee award. But if a key plaintiff and its lawyers at Constantine Cannon get their way, the slog may not be over yet.

Visa, MasterCard, and a group of major card-issuing banks agreed to pay an estimated $7.2 billion to resolve claims that they fixed the swipe fees that merchants pay for credit and debit card transactions. The settlement, which is pending approval by Eastern District Judge John Gleeson, includes a $6.05 billion payment to millions of merchants for alleged past damages and a temporary reduction in fees that’s estimated to have a value of $1.2 billion.