Chance Me for Ivies + T10s (STEM/Business), Match/Safety Recommendations?

Trying to major in both tends to require more than 8 full-load semesters of course work. In addition, some engineering employers are skeptical of college applicants who appear to see engineering as a stepping stone to management (as signaled by lots of business courses).

Which of CS, ME, or business is your primary academic and professional interest?