TPAs owned by brokers, such as Gallagher Bassett Services Inc., the fourth-largest TPA in Business Insurance’s latest rankings, which is owned by Arthur J. Gallagher & Co., or by insurers, such as eighth-largest ESIS Inc., which is owned by Chubb Ltd. and ninth-largest Helmsman Management Services Inc., which is owned by Liberty Mutual Insurance Co., are smaller parts of the total businesses and therefore less acquisitive, experts say.

“Those are the biggest companies that are currently owned by somebody else that could be in the consolidation game down the road,” said Sean O’Neill, a Chicago-based partner with Bain & Company’s financial services practice.