These ten unnamed Leviathans acted as delegates representing various parts of the United States.
Like all of the Leviathans, they came to Earth through Castiel when he absorbed all of the souls of Purgatory. Upon the dispersal of the Leviathans into their own separate vessels, they were not in the same room as each other again for months. Under the command of their leader Dick Roman, each Leviathan was placed in charge of a separate part of the United States.
As Dick's master plan neared its completion, he brought the delegates together for the first time since they were inside of Castiel for a meeting at SucroCorp. Dick outlined his plan to them regarding how the slaughterhouses would work and how they would keep the human population in check. On Dick's order, Royce brought in Polly so that Dick could demonstrate the effectiveness of Additive 3.0 which killed those with undesirable traits, a demonstration that the delegates greatly enjoyed observed, unknown to them, by the Prophet Kevin Tran.
It is unknown what ultimately happened to these Leviathans. The Leviathan master plan fell apart when Dick was killed shortly after the meeting, leaving the Leviathans without a leader. If they were still at SucroCorp when the battle took place they may have been dispatched by Crowley's demons. If they weren't they may still be loose upon the Earth, albeit reduced to little more than harder to stop than normal monsters.