So, I have heard people arguing both sides. Can students actually petition to take any ASE they want or are those exams allowed only for the "traditional" subjects (i.e. 5.111, 7.012, 8.01, 8.02, 18.01, 18.02, 18.03 and 18.06)? In case it is indeed possible to take anyone you want, I would really appreciate to hear from a student who has taken the exam in any other subject! Thanks!
According to the website, it doesn't say that you can only take certain ASE's, or ASE's that are included in the GIR's.
Most freshmen usually ASE out of core classes during orientation, usually 8.01/02, 18.01/02, 5.111, 7.012 (I think the latter two you have to sign up in advance). I chose not to take ASE's because I figured I'd probably take 18.02 anyway (I'm taking 18.022 this semester) and I don't think I have enough knowledge to pass 5.111 ASE.
I think there are just fewer incentives for students to take ASEs outside the GIRs/foundational classes, because prerequisites for other courses are not strongly enforced. If you have, for example, really advanced coursework in math, you're welcome to just start your first semester freshman year in graduate courses. So you'd need to get credit for the GIRs, but you don't need to get credit in Advanced Blah Blah Blah -- you could just take a different class to count toward your major. Getting the required credit to graduate in four years is not the major logistical hurdle.
Also, other ASEs are arranged on a departmental basis, and once you're no longer a freshman, your ASE grade shows up on your external transcript. The math department in particular is also notorious for making you do all of the homeworks to get credit, so there may be some additional hoops that you have to jump through for credit for courses outside the GIRs.
I don't think it's necessarily impossible to take other ASEs it's just very rare and has to be arranged with the particular department. I think someone I know took the 5.12 ASE but more common seems to be simply skipping prereqs and taking the more advanced class anyways.
Some departments will actually let you substitute higher-level classes for requirements. I have a friend who had done a lot of algorithms / math in high school, so instead of the normal sequence of 6.042, 6.006, and 6.046 (they wouldn't give him credit for 6.042, but they saw that he had already taken the material / gotten a good grade) they let him substitute a graduate-level algorithms class instead.