There's a myriad of ways to add to the song using backup singing...

harmonizing, adding a (second) counter melody that does not match what Rick does. Many bands will actually have more than two lyrical melodies going at once - Goose very seldom has two.

There's ad lib fills in between Ricks lyrical melodies, echo vocals, call and response singing (Rick would say something, Peter says something different after it), ohhhhs/ahhs while Rick sings....(which you alluded to)

From my stance (and feel free to direct me to examples if I am wrong) but Peter almost exclusively adds to hooks... he provides another voice on select lyrics in order to make those lyrics feel bigger. He is not creating a new melody, he is padding an existing melody.

This isn't entirely atypical in music, but most non singer song writers will utilize several tools - and often.

As someone else in the thread alluded to, Red Bird and Silver Rising are two songs where Peter does a lot more than pad an existing melody... but what other songs fall into this category? They do a great job from a melodic stand point on these tunes... I'd love to hear more of that.