The College of Arts and Sciences https://artsandsciences.osu.edu/academics/future-students at Ohio State has an exploratory program. They also offer a Personalized Study Program (design your own major). https://artsandsciences.osu.edu/academics/current-students/advising-academics/declare-your-major
Two of Ohio State’s CS majors are from the College of Arts and Sciences - Computer and Information Science (BA or BS) The third CS degree is offered through the College of Engineering - Computer Science and Engineering (BS) The CS classes are run by the CoE, the general education requirements vary between the two colleges. For example, there is a foreign language requirement in the College of Arts and Sciences. CS majors regardless of college can use either colleges career services. “All Computer Science positions are available to both CSE and CIS majors whether they are registered with Engineering Career Services or Arts and Sciences Career Services.” https://cse.osu.edu/current-students/undergraduate/co-opsinternshipsjobs
Moving into CoE is fairly straight forward if your student decides to pursue CSE. "If you are a current undergraduate student at Ohio State, you will need to meet the following admission criteria to officially enroll in the College of Engineering:
C- or higher in Math 1151 (or equivalent); or EM or transfer credit for Math 1151 (or equivalent)
Credit for one of the following science courses: Physics 1250, Chemistry 1210, Chemistry 1250, Biology 2100
OSU cumulative GPA of 2.5 or higher
1 term of full-time undergraduate enrollment at Ohio State (excluding terms of enrollment through post-secondary enrollment programs, such as Academy)
Once you meet the criteria above, you can request to officially enroll in the College of Engineering by contacting an academic advisor in your pre-major of interest. " https://advising.engineering.osu.edu/current-students/major-changers
Moving into Business otoh is competitive - https://fisher.osu.edu/undergraduate/switch-major-business
However, there are plenty of classes open to all undergraduates, I’ve only seen ‘restricted to major’ for upper level courses. So the ability to explore is available. I don’t think there is any subject a minor couldn’t easily be scheduled to complete. There are more bureaucratic procedures at these large schools that are very focused on getting students out in four years, a process helped by identifying a major early. The big schools are mostly interested in getting the right academic advice to students to complete a major. Switching colleges means switching the general education requirements along with specific major requirements.
Have you looked into the actual policies of the big schools he is interested in? Just because business classes are in the College of Business or engineering classes are in the College of Engineering doesn’t necessarily mean students in other colleges can’t take them. Engineering students take science, math and general education classes in the College of Arts and Sciences all the time.