Let's say I asked an interesting question which got a lot of attention and some really good answers. My problem was solved because of those answers and I've accepted one of them. But I want to also pay some reward to the second best answer that already exists on my question. Could I start a bounty for that sole reason? Is it within the site rules?

Does question needs to stay in featured area for 7 days?

If you’ve asked a good question, edited it with status and progress updates, and still are not receiving answers, you can draw attention to your question by placing a bounty on it

But I don't want to grab more attention on the question, I just want to award an existing answer

I've no intention of doing it just now. I'm not even sure I'm able to offer bounties