I was wondering if it would be possible to share profits with a creator whose works are under public domain or the free culture creative commons licenses.
Can you contact them? Then again, I'm not sure I understand your question. Can you expand on this somewhat?
It's very POSSIBLE, but not in an automated way (which I think is what you're asking). You'd need to arrange with them a system of paying what you owe, and it would need to be done manually by you. Of course, you'd need their permission as well.
Sometimes people in this situation write and ask if they may paypal me money. Yes. Yes, you may. Thank you for supporting the arts in general, and my meth habit in particular. All the same, I'm not in a hurry to have a donate button on my site. On the one hand I'd probably get some dollars. On the other hand, do I want to live in a world where everything worth looking at has tip jar next to it? I kind of feel not having that button is a good way to vote "no".
I tried the donation rout and didn't like it. The reason being is people will donate and then expect special favors for their donation. Consequently, I removed the donation buttons so as to not be bothered by people.