Socializing itself doesn't give you a new mission, but is adjacent to two new ones.
The party mission that can net you a lot of captives if you have some good brawler gals, but you must research the party dress first, and the precinct defense, which just puts you against a lot bandits, should be quite doable if you can handle bandit towns, but you need to stop targeting civilian traffic first, the govts won't deputize common robbers