Danny is captured by the GIW, and depending on if it is a good or bad reveal AU, possibly also the Fentons. Jazz, Tucker and Sam do what they can, but they're just regular people going up against a government agency. They need... leverage.
Somehow they find out about the team, either Tucker through his hacking met Hardison online, or maybe one of Sam's parents' rich friends was a target? Either way, Jazz goes to the meeting to beg them to save her brother. Eliot does her Cassanova act and helps her dry her tears.
This is all happening after the fake psychic episode, so the Leverage team thinks the GIW is faking the paranormal activity in order to cover up kidnaping. There's your typical third-act crisis where the plan starts to fall apart because they didn't realize the GIW's tech is actually reading ecto or something. Luckily Hardison manages to pull off some hacking/Parker is able to plant some actual Ecto to get the alarms going.
All throughout Tucker is helping Hardison by filling him in on Ecto-tech, Sam is helping Sophie with the grift (look, she knows how to act like a rich girl to please her parents, she just usually chooses not to.) Jazz is beating people up with her anti-creep-stick alongside Eliot. Dani has a little thieving rivalry with Parker. (Parker says invisibility is cheating.)
At the end of the day, Danny is saved and the GIW in ruins. Sam offers to pay, but they tell her they operate on "alternative revenue streams" or whatever the saying is. So the Phantom team look at each other and nod in understanding. Danny goes into the Ghost Zone and comes back with the ghosts of Nate's son Sam and Parker's brother Nick.
The two dead little boys have become best friends in the afterlife.