I find this is a common problem.
And indeed, the new stories are often very important. Still, that is not necessarily an excuse for adding them (Can’t they wait until the next Sprint? Don’t they want to know what the real velocity of the team is?).
This is a complex problem.
But sometimes it is as simple as…Tell Her No. This is a song by The Zombies. A little fun might make it easier to say No. See here. (And remember the ever-friendly quote: “What is it about No you don’t understand?”)
While we must be compassionate (do I always say No when I should?), still we must say No more. In a nice way. My Yes means very little if I can’t say No. I recommend this book by a friend of mine. Bill Ury also co-wrote Getting To Yes.
Again, No isn’t always the right answer. This is a more complex problem.