@nella2024 well that doesn’t really answer the question, does it? I do not know how UCI does class scheduling as their website is not very clear. They may have changed their policy or the person presenting at the honors program 3 years ago could have quoted the policy wrong. I don’t want to mis-lead you.
UCD has a pass time when you can sign up for up to 17 units in any college/department. Some (few, mostly upper div) classes are restricted to students in certain majors. Priority registration would allow you to sign up for any non restricted class before other students. The second pass time allows one to sign up for classes that were restricted during the first pass time and allows you to sign up for up to 19 units. UCSB limits the units you can sign up for in your first pass time to 13.5 units. UCSD is similar to UCSB in that they limit you to 11.5 units during the first pass time. Their website says that they also check major, college and class standing in determining registration restrictions.
UCSB: https://www.registrar.ucla.edu/Registration-Classes/Enrollment-Appointments/Enrollment-Appointments
UCI: https://www.reg.uci.edu/enrollment/windows.html
UCD: https://registrar.ucdavis.edu/registration/register/pass-times