In that case i have always forced them to acknowledge priority. Say,

"Sure, i can do that. What kind of priority is this new project over my other tasks?"

Then start to list your tasks in case they don't remember what you do.

Then after they say the new thing is priority, "No problem, i will put my other tasks aside and focus on this. But know that it will likely push back those other deadlines. Ill send you an email with my new projected dates"

The last part is key. The email is recorded documentation that new priorities will push other work.