Certainly! One example of a phrase or saying that expresses when someone wants another person's happiness more than their own is:
"I would give up my own happiness just to see you smile."
This saying highlights the depth of one's selflessness and their willingness to sacrifice their own well-being for the sake of another person's happiness. It emphasizes the idea that the speaker's primary concern is the other person's joy and contentment, even if it comes at their own expense.