I figured out a trick but I don't know what to call it. Jump cancel? Fall cancel? Attack cancel?
First, you need to stand on a platform. Moving ones like Smashville's work best.
Next, drop down by flicking the control pad down.
Now you can press any command. Timing is crucial: you must still be on the platform but no longer standing on it.
I use Jab (Neutral A) since that seems to be the easiest. If done correctly, the character will fall and then appear back on the platform without jumping.
Smashes are very useful when performing this. However, they have the hardest-to-see results. Try in slow motion to somewhat see it clearly.
If you're good at it, you can move your character around the platform quickly, and use tilts as well. This works with all characters.
EDIT: Most of these won't damage the opponent, but some (like Smashes) will. It works when landing on a platform too.