LEXINGTON, S.C. — The table festooned with red “Carly for America” placards arrived hours before the candidate. Political operatives took up positions outside the front door to catch supporters of Carly Fiorina, the corporate executive turned Republican presidential contender, and gather their contact information before steering them inside to the room where she would speak.

But the table, the placards and the workers did not belong to Mrs. Fiorina’s campaign. They were there because of the “super PAC” supporting her run for president.

The Federal Election Commission forbids direct coordination between campaigns and super PACs, lest candidates effectively rely almost entirely on the huge, unlimited donations of a small number of billionaires. But in 2016, the groups are aggressively exploiting gray areas and loopholes in the rules, few of which the commission — deadlocked with its three Republican and three Democratic members — has hastened to close.