Creative License:
Despite searching, I can't find anyone who has done this. The only weights you can put on an atlatl are about mid-shaft and then only about 85 grams. The shaft of an atlatl, to be efficient with such lengths, seems to need to be as light as possible.
So to make it a melee weapon, we'll need to be creative.
In any case, your shaft needs to be made of something REALLY strong and REALLY light. Even with that, it's likely that the kind of abuse it will take as a melee weapon will damage the spear-throwing ability. A shaft of normal materials might still work as a club and an atlatl, but it would likely do one job, the other or both poorly.
Have you considered a punch-dagger? The handle where the person holds the atlatl would have a grip that included a strong hold and a built-in piercing weapon. This would give the fighter an emergency weapon in desperate situations and look really bad-ass.
If the shaft were REALLY (handwavium) strong and flexible, the punch-dagger could double as the business-end of a spiked war club. Or an axe, if the punch-dagger were shaped like an axe head. In this case, there would be a grip at both ends. It would still only be a light melee weapon. A dedicated weapon would work better.
A thin spike on the end of a strong shaft could be used foil-like as a stabbing weapon. It would likely wreck the atlatl function, and the atlatl part might cause it to stick in an opponent. Or a spike on the handle end could work like a knife to stab (rather awkwardly).
A chain attached to the grip-end of a strong atlatl could be attached to a flail head. While it strikes me as awkward, most of the weight of the flail would be away from the arm. Then the mid-shaft weight could functionally be a second handle to allow the flail to be swung about two-handed.