Can a Muslim man marry a non-Muslim (and non-Ahl-al-Kitab) woman?

I know from other questions on this site that Muslim men can marry Jewish or Christian women , that Muslim women can't marry non-Muslims , and why there's a difference in marriage law for Muslim men and women . I've also learned a good deal about temporary marriages , but this question is not about that. My question is, can Muslim men marry women who are not Ahl-al-Kitab? That is, can a Muslim man marry a woman who is either atheist, deist, polytheist, pantheist, Zoroastrian, or anything else I haven't thought of? Since Hanafi is the school of Fiqh with the greatest number of adherents, I'd specifically like an answer from that perspective. But if you could give a quick note about how widely-accepted your answer is from the perspective of the other schools, that would bring your answer from good to great.