@underscoreone - You should call or email them. Many times there is a placement test that you can take to prove your readiness for the course you want to take.
@underscore you can also consider doing a summer course for college credit in something you are interested in. Of course, that will be a lot more expensive, but they are fun and you learn a lot. My D did a CS summer course for credit at Carleton College. It was a selective course, and she needed tescher recs to be accepted. It might be a bit late now to organize because the good ones are selective, but you can find all kinds of courses for college credit. It won’t give you an advantage (pay to play,) but it does at least show that you pursue your interests outside of high school and you will also possibly use it as a prerequisite in college. You will also likely get a good professor rec too. I recommend it.
@Lindagaf Yes, I have heard about college credit courses. I was debating for a while whether to take a Columbia CC course, but ultimately decided against it (although I could have easily gotten the recs). The tuition is pretty extravagant ($6k!), and as you mentioned colleges don’t view you more favorably for taking it. Plus, I’ve heard from elsewhere on CC that the course isn’t actually selective/prestigious-- yes, they require teacher recs, but they accept most people who apply because they want the money. Not to say that the courses aren’t fun/interesting, though.
I am already going to a math program by NYU for 3 weeks in the summer, too. While Columbia’s doesn’t strictly overlap with it I would have to put in a lot more hours of studying throughout the morning/night.
It really does depend on the college as to how they structure the program and how they select students. There is huge variation. Often, a program is not even run by the college where it’s being held, but an outside company. As you are already doing a summer academic course, another one would be excessive.