TikTok Inc. may have reached a confidential settlement to resolve lawsuits brought over alleged privacy violations, but a duel for leadership that is escalating this week among plaintiffs attorneys could upend the deal.

The class action settlement reached last month involved a group of plaintiffs firms led by Katrina Carroll, of Carlson Lynch in Chicago, and Jonathan Jagher of Freed Kanner London & Millen in Conshohocken, Pennsylvania.