EX 3:1 Jethro was the father-in-law of Moses.
NU 10:29, JG 4:11 (KJV) Hobab was the father-in-law of Moses.
This seems to suggest that he did. Curious if anyone else has looked into this.
About Jethro, Wikipedia states:
There is some disagreement over the name(s) of Moses' father-in-law. In the KJV translation of Judges 4:11, a man named Hobab appears as Moses' father-in-law, while Numbers 10:29 makes him "the son of Raguel [Reuel] the Midianite, Moses' father in law". Reuel is noted Exodus 2:16, as "a priest of Midian" who had seven daughters. Exodus 2:18 "the girls returned to Reuel their father". Reuel becomes Moses' father in law in Exodus 2:21 "Moses agreed to stay with the man, who gave his daughter Zipporah to Moses in marriage."
In Numbers 10:29, the Hebrew for the name Raguel is the same as the Hebrew for Reuel. The reason for the difference is that the Hebrew character ע (ayin) in רעואל is sometimes used merely as a vowel and sometimes as "g", "ng", and "gn", because of the difficulty of its pronunciation by European speakers. Re-u-el, with the first syllable strong accented, is nearer to the true pronunciation. Some suppose he was father to Hobab, who was also called Jethro, a likely possibility.
Another thing to consider is that there is only one Biblical Hebrew word for both "brother-in-law" and "father-in-law" (chathan). It is, in fact, the word for any and all relations by marriage. If one takes into account the Biblical custom of multiple names for one person as well as Numbers 10:29 calling Hobab Reuel's son, Reuel and Jethro both appear as Moses' father-in-law, while Hobab may be seen as his brother-in-law. However, this is disputed among theologians.
An example of a theological position about the issue can be found in this paper. The author argues that the contradiction is apparent. He states (p.9):
The information which has been preserved in the traditions dealing with Hobab can be best understood to say that Hobab, son-in-law of Moses, was a Midianite belonging to the clan of Reuel and a smith by profession. Jethro, priest of Midian and father-in-law of Moses, was a member of the same clan (Reuel). Although their roles have been somewhat confused in later reflections of the early Israelite traditions, there is still enough information preserved to suggest this reasonable solution to the puzzle.
Details are in the paper, but for example he suggests that their profession (as stated in the Bible) were too different for them being the same person. I quote (pp.6-7):
the roles of Jethro and Hobab are entirely different. Jethro appears as an old man with seven daughters (Ex 2,16), who advises his son-in-law from the wealth of his own experience (Ex 18). Hobab, on the other hand, appears as a vigorous younger man whom Moses wishes to act as guide in the wilderness (Nm 10,29-32) ...
We have only to change the vocalization from hôtën to hätän where Hobab is mentioned, and our difficulties vanish: render Nm 10,29, "Hobab, son of Reuel, the Midianite, son-in-law of Moses." The fact that both Hobab and Jethro belonged to the clan of Reuel should cause no difficulty whatsoever, since the West-Semitic nomads were as a rule endogamous, so one would expect Moses' son-in-law and father-in-law both to come from the same clan.
The previous answer deals ably with the matter of the name of Jethro.
But the main question (Did Moses have more than one wife in his lifetime ?) opens up another factor.
It is my understanding that Moses married again after the incident concerning the circumcising of the child born to Jethro's daughter, Zipporah, who was displeased regarding circumcision. Exodus 4:24-26.
Then Zipporah took a sharp stone, and cut off the foreskin of her son, and cast it at his feet, and said, Surely a bloody husband art thou to me. [Exodus 4:25 KJV]
Moses sent Zipporah away as is recorded in Exodus 18:2 when Jethro brings her back again. My own assumption is that Moses responded to Zipporah's displeasure and sent her back to her father. But Jethro was able to encourage her to accept her situation and he brought her back to Moses in the wilderness.
Then Jethro, Moses' father in law, took Zipporah, Moses' wife, after he had sent her back [...] And Jethro, Moses' father in law, came with his sons and his wife unto Moses into the wilderness, where he encamped at the mount of God : [Exodus 18 : 2 and 5]
In Numbers 12:1 we read that Miriam and Aaron spoke against Moses because he had married an Ethiopan woman.
And Miriam and Aaron spake against Moses because of the Ethiopian woman whom he had married: for he had married an Ethiopian woman.[KJV]
My own assumption is that Moses married a second time, perhaps while Zipporah was in departure from him.