I was reading Numbers 12 and some questions came up. Did Moses have more than one wife? Was Zipporah a Cushite? -- Mike C.
It seems to me that Zipporah was a Midianite and thus not a Cushite (Ethiopian). Moses had been married some time when he took his second wife. A number of powerful men in the OT had more than one wife (for example, Abraham, David, and Solomon). Not that God approves or commends polygamy. It wasn't against the law back then. There are several articles at my website touching on polygamy.

If my answer is too short, I found a good explanation here: https://gotquestions.org/Moses-wife.html. (I think his analysis is solid.)