No school can prohibit a student from taking outside classes. They can reserve the rights to what is reported on their transcript. They can prohibit missing school time. Colleges can and will look at education beyond the HS a student is enrolled in. Excellent idea to expand upon your son’s capabilities. btw- in a heavily Catholic area most kids went to the good WI public schools- they offered better academics and those who wanted it still got plenty of their religious way of life.
Why NOT take two sciences, (and adding math classes) at one time? No different than taking any other subjects such as two that include writing assignments. I get so tired of people who treat STEM as though it is more difficult than other subjects. A student who enjoys and is good at science and math will thrive with more of that. It would be torture to substitute nonfavored subjects because some people think they can’t enjoy as much STEM as possible.
It is a good idea to take more Spanish to be more competitive for many colleges. UW-Madison requires two years but notes that most will have had four as I recall. Finding a way to make his school year enjoyable and still get foreign language credits is great.