However, this is no longer possible now for my younger siblings enrolling at the same public high school. Apparently the school now put much more strict limit on pre-requisite and what classes students can take at which year. There is now much less flexibility.
This is not due to significantly increased student body size , but mainly for "equity" in education outcomes -- i.e. holding back the advanced students to accommodate the less advanced students. It makes very little sense, but that is California!
For my school district, the general tendency is that you had a "core" of mandatory classes where your choice was at best "do you want the hard or easy version of the class", although math in particular was tracked somewhat more independently of grade level. In addition, there is a set of elective slots, and degree requirements might strongly push you to certain electives (in particular, foreign language elective requirements are probably pretty common).
Doubling-up on two sciences in one year wouldn't be normally possible, at least on the standard end-of-year sign-up-for-the-next-grade forms, but it is possible to do so if you bitch long and hard enough at a school counselor for special dispensation.
At my local school, there was an extra early bird period in the morning if you wanted to take an extra class. We could also take classes from the local community college and have them count as both high school credit and college credit (today, the high school I went to has moved and is now sharing a property line with the community college, so it makes it very easy for students to go back and forth). My niece just graduated from high school two years ago and she's pretty close to finishing her bachelor's, because she had earned a lot of college credit already. For motivated students it really works out great.
In high school, the majority of your schedule was in required classes. In college, the vast majority was in major courses / electives.