Has any rabbi in Talmudic days had more than one wife at a time?
I don't know of any record of this. In fact, the Talmud frequently mentions a rabbi's "wife", meaning he only had one.
The only instance of rabbinic polygamy in the Talmud [Yevamot Y 4:12] was Rabbi Tarfon, who married 300 women when there was a famine in the land, so they could eat. As a kohen, he received the priestly tithes, which he could share only with wives and children. However, this was clearly just a legal fiction, intended to allow the women to eat during the famine. Rabbi Tarfon had only one “real” wife, as the Midrash Rabbah and Talmud Yerushalmi make clear:
When the wife of Rabbi Tarfon died, after the grave had been filled in, he said to her sister during mourning, “Marry me and rear your sister's children.” But although he married her, he did not consummate the marriage until after thirty days. [Ecclesiastes R. 9:8]
On festivals and holy days Rabbi Ṭarfon was accustomed to delight his wife and children by preparing for them the finest fruits and dainties [Pesachim Y 37b].