Jack Harkness: Sectors 0-2 Leader, Interview Team, Investigative Team (mainly tech)
Okay, so, checking out the roster I see at least three people in Jack's team that he's never interacted with and whom I know nothing about, so a mingle would be a really good idea to rectify that, at least in part!
As for the rest of it, Jack normally checks in at DF HQ most days, so feel free to assume you've bumped into him on occasion there. He also patrols a lot. Unlike Kitty, he's pretty lax about training exercises for his team, but he's always willing to spar or give people tips or whatever if asked.