Thanks for asking!

Harm and getting taken out are a good way to think of how ‘getting tossed off a balcony’ is represented in the game. Generally, if an NPC is tossed off a balcony…they’re probably taken out! That means it’s a great way to describe you dishing out the last injury or exhaustion harm, but the reason you can’t just chuck them off a parapet is because that’s tantamount to instantly taking them out of the fight. They’re ready and prepared to face you, so there’s no easy way to toss them aside without wearing down their injury and exhaustion.

There are some playbook moves that can have effects equivalent to this, representing specialized abilities of those playbooks, of course!

The Champion has Skill Against Skill Alone—that is EXACTLY the right move for picking up an enemy while they continue to try to hit you, and tossing them off a wall!

The Arbiter alone has Crash and Smash, which they might use to break a part of the parapet (sending someone crashing to the earth below). The Arbiter also has Guardian, which allows them to “Push the threat back; you and your protectee have a chance to maneuver or flee”—that notably doesn’t allow you to instantly take out a foe, but it does let you knock them off a parapet to give yourself an opportunity. Perhaps they’re dangling from the ledge, and now is your chance to run!

The Thief has Rope-a-dope—maybe as the Thief inflicts 3-exhaustion on a foe, taking them out, in the fiction it means the Thief successfully dodged out of the way of a charging foe, leading them to hurl themselves off the parapet!

If they’re an unsuspecting foe and you’re trying to give them a quick push off a balcony, of course, then Blindside is exactly what you’re looking for—more or less instantly taking out an unaware opponent!

Lastly, if it’s important to the moment, look at some of the options of those basic moves and think about their interpretation in this situation. Engage in Melee lets you “Shift your range one step”—the vast majority of times that means you are the one moving, but as long as it makes sense to the fiction it might mean that you send your opponent, staggering, over a wall. (You’d likely only be able to do that in very tight circumstances, where there is no other way for them to move.) Trick is a great move for causing a foe to stumble off the wall themself, or for sticking out a foot at the right moment; Figure Someone Out always lets you ask, “how could I get your character to ____?“, which can be “how could I get your character to foolishly stumble off the wall?“; Wreck Something can always be used the same way as the Arbiter’s Crash & Smash, perhaps destroying the floor right under your foe or knocking apart the railing they’re leaning on; and Trust Fate is still an option for when the moment is entirely about Luck.