Nothing wrong with being a 16 going on 17 year old and being a freshman on campus at a flagship U (globally gifted son did that for UW-Madison). It is good to also have a well rounded education to prepare yourself for a good college and life. Music, arts and more social studies and humanities as well as math/sciences. A foreign language. Sports/athletic time. Be sure to educate yourself in more than just STEM interests. Being home schooled and in a metro area allows you time to accomplish as much of these as a student exposed to a regular HS experience.
^^Yes. I get that OP loves math and seems more interested in learning than credits (and that’s what he’s asking about)but I would also encourage him to use some excess brain power on another subject. With perfect hindsight I really wish my kids had achieved true foreign language fluency in HS. It would have saved older D 4 semesters of a class she didn’t like. Many colleges have gen ed requirements in that area. D2 only had a 2 semester requirement and ended up taking Russian and loving it. Maybe some of you already know this, but when she started exploring grad programs, many PhD programs in math required proficiency in languages usually preferably Russian, German or French. So if OP even thinks PhD may be in his future, working on language may be helpful or at least save him time in college. D2 also took Greek. She liked it also. Think the fact that Greek and Russian had different alphabets appealed to her math brain and it was more like puzzle to decode. Obviously a long way off, but OP sounds like one smart kid.
Thanks to everyone for their advice! 
@ucbalumnus: I may have enough depending on how I pick my classes for the next few semesters, but I’d really like to take the time to explore more before I go to college. Thank you for all your help!
@DJCordeiro: Thank you for the suggestions! I wasn’t aware that there were summer math programs so close to us, and I’ll add it and your other points to my list of things to research. 
@wis75: Graduating early is an option I’ve considered, but not the one I’m leaning towards at this point. I’m happy to hear it worked out for your son, and also to hear that being younger isn’t too much of an issue at college. I definitely do enjoy humanities classes (this year it’s AP Lit and APUSH), and am planning to take several more in the next few year. Thanks!
@scmom12: (I figured I should clarify that I’m a girl since it’s hard to tell from my username ) I have been taking Chinese for many years unofficially, and I believe I could take AP Chinese next year if I really tried. I probably won’t, just because there are other subjects I’d rather focus on, but I will try to do it or at least get to Chinese 4 by the time I graduate. I don’t think I’ll be taking a different foreign language, but I will think of it, and thank you for sharing your experience!
As for other subjects, I really enjoy English (took AP Lit and there’s one more CC English class) and I like the history class I’m in now (APUSH). I’m also really hoping to take economics, psychology, US/world politics, and possibly another history class.
I don’t think I’ll be doing a PhD–more likely going into mechanical/electrical engineering or CS–but I will definitely consider your advice in case I change my mind.
You could try a real analysis class, which should be useful to any program you’re considering. Beyond that, for CS you might try Combinatorics, Graph Theory, Linear Programming, or Numerical Analysis.
For the Chinese language, you could also check local colleges to see what level you place in the language, and then complete that level of college Chinese language. Note that this includes the community colleges, some of which (e.g. Laney) have at least four semesters’ worth of Chinese language courses.
Consider adding some arts and sports. Well rounded includes nonacademic classes.
You’ve gotten some great suggestions here. I’d make one additional recommendation, eIMACS, for both computer science and mathematical logic. My daughter, also homeschooled, is taking their University Science courses rather than AP CS, and though you’ll have taken the latter, I don’t think it will be redundant:
http://www.eimacs.com/parent_ucs_overview.htm#UCS1
They have a three-course series in Mathermatical Logic, which she is enjoying also:
http://www.eimacs.com/parent_aml_overview.htm?navname=PARENTS&toopen=ul1,ul3&scrolly=277&subnavid=a4
After those classes, a typical student would start into something along the lines of real analysis, or perhaps abstract algebra. There are a lot of different math tracks though. Some math majors go all out in analysis, some lean towards algebra, others lean toward geometry or statistics, or actuarial science. It really just depends on where your interests are at and what you intend to do in college.
However, you’re not likely to find anything beyond Calculus III, Differential Equations, and Linear Algebra at a community college. They typically offer other math classes like discrete mathematics and finite mathematics and things like that, but those aren’t really “after” Diff EQ or Linear Algebra. Those are just for people on different math tracks (mainly computer science related fields). In either case, you are VERY well ahead of the curve with your level of mathematics. My main concern would be with the amount of depth in each respective subject. Mathematical maturity is something that comes with time. I’m a math tutor, and I’ve seen instances of students cramming far too much math in during high school. They often learn the stuff well enough to pass the tests, but they often tend to not really “get” the mathematics. They understand how to work through the mechanical process, but they don’t understand what the math really means or see what the equation is telling them. This may not be the case for you, but it’s a point worth considering.
If you aren’t able to find actual courses to take, definitely do some independent study of some more advanced math…but also go back and brush up on some of the math you’ve already done. You’ll thank yourself after realizing how much of it you’ve forgotten. I’m currently tutoring a student in calculus II, and I’ve had to brush up on some of the more obscure methods of integration because I simply haven’t encountered them since taking calculus II myself.
One thing I would consider is taking your SAT or ACT and the Math 2 subject test soon. Some students get so advanced that they forget details because they learned this material so long ago. jmho
@Vladenschlutte: Thank you for your advice–I’ll look into those classes and see where I can find them!
@ucbalumnus: I’ll look at other community colleges, but I believe the ones that aren’t too far to drive too don’t have more than one year of Chinese. I’ll definitely do more research on it though, and thanks for the suggestion.
@wis75: For ECs, I’ll consider my main ones (outside of robotics) to be Bobbin Lace (a fiber-lace art–learning and teaching), ping-pong (recreational), and Aikido (learning and teaching). I really enjoy both, but I didn’t include it in my earlier posts because I didn’t think it was as relevant, but now I see that it made me look sort of skewed.
@hs2015mom: Thank you for your suggestion! I will defintely look into eIMACS, and both the classes sound really interesting.
@comfortablycurt: Thanks for sharing your experience–I didn’t really consider it, but now I will make sure to review the math I’ve done in the past. I’ve talked to the community college about whether I could be a math tutor, but even with the math tutoring center, one of my past math professors (and apparently his boss) involved, they couldn’t figure out what paperwork I needed to do…I hope it works out, since that would make sure I remember the material!
@Much2learn: Because of the timing of the robotics build season and competitions, I’ll probably be taking the SAT this June, and the Math 2 subject test in October / November (depends on PSAT schedule, I guess). I looked at some tests, and there’s defintely some review I’ll need to do! Thanks for the reminder!
There are great summer math programs. My son did PROMYS. There is Ross. I’m sure at Art of Problem Solving there will be discussion of different programs. If you enjoy math competitions you could see if there is an ARML team in your area.
If you are not interested in early college, have you considered doing something completely different. You could look at a year study abroad, particularly if you are interested in languages. It sounds like you have plenty of credits to get your HS degree thru your homeschooling. You don’t need to rush to college take some time to really explore an interest.
You could also apply to colleges next year and then hold off a year on attending.
@Python20: Thank you for your suggestions! I’ll do a bit of research into the summer programs and math competition, but I’ll probably stick with regular classes so I have time for other activities. I hadn’t considered a year abroad, but I will. I probably won’t apply next year just because I’m not sure if I’ll be ready (have the proper paperwork / classes / tests), but I didn’t know that I could hold off…I will consider that. Thanks!
Has anyone suggested SUMaC as a summer option?
@Hoggirl: Thanks for the suggestion! I’ll add it to my list of summer programs to look into.