My daughter just graduated from a Tech school in engineering. While something like 75% of students are in STEM, the school does offer business and psychology as very popular programs.
Daughter did not have a minor and it would have been very difficult to have a minor in something other than chemistry or physics or math. There just aren’t enough electives in the engineering programs to fit in a minor in an entirely different subject without staying in school for extra semesters or doing summer. Most kids are more interested in using extra time for internships or co-ops than in just taking more classroom work.
Her boyfriend was a construction management major and did take business classes. He also got an MBA after undergrad so clearly didn’t have enough business classes for his needs.
A small tech school isn’t the right choice if you want a lot of humanities classes or music theory as a minor, but most have enough non-STEM classes to kept college interesting. If you really want a business degree and an engineering degree, then pick one of the bigger schools like VT or GT and plan on staying a couple of extra semesters.