For an example of what I'm talking about, look at the end of Act II in DA2. Then consider that whole series of events with these additions:
1.) if you made nice with Seamus between when you rescued him early in the game and when the Qunari representatives vanish, you get a mid-act message from him saying "Hey, I'm going over to the Qunari but this Mother Petrice chick has showed up and wants me to go talk to my father first, should I go?"
2.) You THEN get the "go save the Qunari representatives" quest from the Viscount.
3.) You now have to make a decision . . . do you go find Seamus first or do you try to locate the Qunari representative?
4.) If you go find Seamus you can tell him "Mother Petrice is a Qunari-hating zealot do NOT have anything to do with her" . . . but by the time you catch up with the Qunari representative, it's too late and they all get killed. But Seamus doesn't leave the Qunari and doesn't get killed in the Chantry. And neither does Mother Petrice.
So now you have a branch. On the "save Seamus" side, when you show up at the throne room to confront the Arishok, possibly Seamus is there and so is Mother Petrice. The Qunari reps are possibly dead or still alive. So, now you can have a TON of different options here:
1.) Depending on how you've handled things thus far, the Arishok still kills the Viscount and does the head-throwing bit. Live Seamus freaks out and the Arishok kills him, too. Live Mother Petrice uses this as an opportunity to rally her followers against the Arishok and the scene turns into a massacre where you pretty much have to kill all the Qunari. Mother Petrice also gets killed during the fighting.
2.) Seamus convinces the Arishok NOT to kill the Viscount because of how you've handled things. Mother Petrice rallies her followers against Seamus the Qunari-lover. THEY kill the Viscount and Seamus. YOU kill Mother Petrice and then you have a chance to deal with the Arishok viz Izzy and the Tome of Koslun.
3.) As 2 but instead of killing Mother Petrice you side with her and kill the Arishok et al. During the battle she gets hacked down.
4.) If you save the Qunari rep instead of Seamus, Seamus' death plays out pretty much as it did in DA2, but you can optionally save Mother Petrice from the Sten that shows up to shoot her. If you do this, she rallies her followers against the Qunari and instead of the scene with Aveline you have a scene where Petrice's followers assault the Qunari compound and get butchered, leading into the throne room confrontation. You can minimize duplication of effort here by having the assault take place offscreen and having the Aveline scene go forward, it's just that she's complaining about the death of Petrice and followers instead of miscellaneous unnamed elves of no previous importance.
5.) As 4 but you let Mother Petrice get killed. Throne room scene plays out as in DA2. If you duel the Arishok or let him have Izzy, the Qunari reps thank you for saving their lives and give you some kudos for not being a dipshit.
That's a LOT of permutations but the result is the same: Qunari out of the city, Viscount removed from power. But boy wouldn't that have felt like you had a big impact on the result vs. "sure, take Izzy" or "nah, Izzy belongs to me". They could have even added a further level of permutation where you actually have a chance to get the book from Izzy instead of her running off with it, so if you handle the Qunari situation well and save the Qunari reps, you can hand over the book to the Arishok at the Aveline scene and there's no throne room scene AT ALL. This isn't necessarily the "best option" because Seamus has to die . . . but it's the option with the smallest degree of "people getting butchered". Or do a second permutation where if Seamus is alive and you hand the book over during the Aveline scene, Seamus convinces the Arishok to forego getting Izzy and sends YOU to go "take care of" Mother Petrice. (if you refuse this option you get to duel the Arishok.) So, in those two options Viscount Dumas survives . . . and promptly retires, either because his son is dead or because his son has gone over to the Qunari.
The main result of all those permutations--Qunari out of the city, Viscount removed from power--is EXACTLY THE SAME. But you had a *significant* effect on the life and death of a BUNCH of people that wasn't "hand over Izzy and she escapes in the epilogue" vs. "don't hand over Izzy and kill the Arishok."