Well, using the old Indy bookends and the last two movies as a jumping off point:
He will go on, at least, one more adventure. One where he has his right eye cut out.
Not long after the events of DoD, a young redhead named Sophie will show up on his doorstep. If you want to tie it into the events of the movie, she heard his name on the news, and decided to seek him out. She reveals herself to be the daughter of Indy, together with a redhead whom Indy slept in the mid-1940s (maybe Sophia Hapgood? It would motivate the name "Sophie". Though, I could see other candidates). Mutt is a precedent of something like this happening in indy's life, it can easily happen again.
Motivated by this second child showing up (out of nowhere) on his doorstep, Indy sets out to contact all of his past sexual partners, and discovers that he has spawned a number of children (spread across the world, and different ethnicities) between 1917/1918 and 1958 (1957 (KotCS + nine months)), several of the older ones have young children of their own by the time that Indy seeks them out.
Seeing Sophie, and her half-siblings, as a second chance, he decides to commit himself to his new children and grandchildren. The do-over that he will never have with Mutt. Though, speaking of Mutt. Indy and Marion discovers that, years earlier, Mutt has himself gotten a girl into trouble, and kept it secret from Indy and Marion. Enter Mutt's daughter, Caroline Jones.
In the 1970s, Sophie has a son, whom later becomes known as "Spike". In the 1980s, she has a daughter named Lucy. Around the same time as the latter, Caroline has two children named Harry and Annie. Over the span of these years, Indy begins recounting his adventures to his children, grandchildren, great grandchildren, even total strangers.
Marion might pass away prior to the early 1990s, explaining her being gone in the bookends.
Closing in on his 100th birthday, Indy ends up going on one last "one last" adventure, where he ends up falling into the Fountain of Youth... and emerges looking like Corey Carrier. Which is then followed by another century of adventures.
The last paragraph is mostly intended as a joke, but it would be a more interesting ending than old Indy simply dying in his sleep one night.
