I suggest checking the web pages of each college or talking with admissions reps.
The scope of your question is pretty broad, and just because it is possible does not mean it is easy. You need to do your own due diligence if you want to be sure your son won’t get shut out of his major or that policies haven’t changed at each college.
I can tell you that MIT will let you major in whatever they offer. Others on your list make you apply to a particular college/department.