Is it possible to change a non-profit employer to for-profit employer, when you have a H1B from non-profit employer?

Question

I am curious to know if my H1B is filed (and issued) by a non-profit employer, can I change my employer and work for a for-profit company with same H1B visa. How should I approach H1B transfer? Am I supposed to apply for new H1B visa even if my current H1B visa (from non-profit employer) is still valid?