How do you go beyond being "just friends"?

There is no way around this. All you got to do is ask her. Just be straight with her ask her out on a date. Its a lot better to be upfront and honest from the begging as she will appreciate it more. If you really wanted you could even make a joke out of it by saying something like "I see you more than I would see a girlfriend if I had one" or even ask her "from a girls point of few do you think I'm boyfriend material" then she will give you her honest answer and then tell her she is girlfriend material and that you's should hook up. good luck

You could try giving her hints that you like her as more than your friend and then you could see how she reacts to it. Also another way to know if she feels more than what she's letting on is if she acts different with you. Like guys act different around the girl he likes, girls do that too. Pay attention to see if she flirts with you or acts differently with you then with other guys. You could also just ask her if she likes you.

pus a little past the friend zne and see if she gets a little freaked out then back off but if sh doesn't push twords a relationship good luck to you