Even though I'd change a few things about it, I wouldn't mind if they used a story similar to my entry for the Indy 5 contest a few years back...
Indiana Jones and the Lost Temple of Time
by Andrew Rhodes
1963: Point Glyphadia near the Greek island of Antikythera. Armed with only a spear gun, Indiana Jones explores an ancient shipwreck and discovers the Antikythera Clock. The device is an astronomical clock that points the way to a lost, advanced civilization.
A run in with a large squid and band of pirates leads to a shocking discovery for the adventurer: the pirates are being guided by none other than Mutt Jones, Indy's estranged son. Mutt steals the artifact from Indy and escapes.
Indy learns that his beloved Marion has been keeping Mutt's involvement with the seedier side of humanity a secret. Seems he's in too deep now, with no foreseeable way out.
Mutt's employer, a Russian super-agent, wants to use the device to locate the lost civilization, but not for academic reasons. Legend says there's a temple there that was actually a portal through time and space. Mutt has a debt to pay, and an eye for the leader's fair daughter. In too deep indeed.
And so the race is on, Father versus Son, from the ruins of Greece, to the misty booby-trapped castles of the Carpathian Mountains, where Indy is trapped in a vampire bat-filled catacomb.
Finally they reach the lost island off the Coast of Antarctica. A ski mobile chase across ice bridges leads them to ruins and frozen remains of a civilization like we've never seen before. At the center of it all is the Time Temple itself. By way of this Time Temple, the climax finds Indy on a dizzying tour/chase through the golden ages of the very civilizations (Egyptian, Mayan, etc.) that he has devoted his life to understanding. His entire legacy right before his eyes.
Along the way, Father will reconcile with son, using their combined talents to save the world and their family once more.