One option could be homeschooling and finishing up high school with online high school programs, plus, perhaps, MOOCs from universities and some independent study to engage in their intellectual interests. The more flexible curriculum could also be coupled with volunteering at a nonprofit, taking community college classes, working in a research lab, or doing other long term projects that don't mesh well with school.
I know two people who have done this and think very highly of this option. The first had severe health problems that made it impossible for her to finish high school in a traditional school, so she enrolled in an online program through Stanford to finish high school. This worked well, because she was in an out of the hospital a lot during high school, and the online coursework allowed her to catch up in a way that a public school wouldn't. The other went to a highly competitive magnet school and felt like it was no longer intellectually engaging, because it was competitive but overly pre-professional/focused on getting As/getting into ivies. She enrolled in an online accredited correspondance program to finish up her coursework her senior year and was able to focus more on specific intellectual interests of hers and start a community service project. Both of these people were incredibly self-motivated, self-directed types, and the one who left the magnet program was somewhat of a "free spirit." However, she also realized that she needed to get certain coursework done (like, not blowing off math even if she considered herself a "humanities person") and do SAT prep to get into a competitive college, and was mature enough to do this outside of the structure of a traditional high school. Both of these people went on to excel in college and their careers, probably in no small part due to the fact that they were incredibly mature and self-motivated.
If you have an exceptionally self-motivated child who would thrive with this sort of intellectual freedom, then I would consider it as an option. They need a compelling reason, and would need to be mature enough to keep studying without the structure/peer influence of traditional school. You would also need to have a plan/curriculum, etc. to ensure they really are getting an education, especially a well rounded education. I know one person who was "home schooled" who basically didn't do anything except read fantasy novels and basically never learned how to do algebra or learned much about history, science and didn't read literature that challenged her. I think if that is what is going to go on during homeschooling, that's a disservice to your DC.
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