Having multiple wives is categorically forbidden under the prohibition of Sfichas Damim. Some divorced poskim forbid even a single wife under this prohibition. I believe the Halacha is like them….
Anyway, the Baba Sali had three wives – in succession. The first two died. He never had more then one at a time.
In addition, it is clear from Chazal that though it was permissible, it was not commonly practiced, from the fact the Gemara refers to women as “D’Bishu R’ Chasidah” etc., assuming that only one woman could hold that title.
The Peleh Yoetz – it’s clear that having two wives was practiced, but he strongly advises against it.
Care to source the Goan & R’ Ovadia? ( R’ Ovadia is in favor of re instituting Yibum, as it the ruling of shulchan aruch that it should be practiced when mutually desired, but that is a totally different bowl of chulent).
Once upon a time a man had the depth of self to be a husband to more then one woman (while a woman, by her very nature, is always totally given to a single man).
Rabbenu Gershon saw that we are far smaller, and hence forbade a man from having more then one wive – a man barely has the capacity to treat one woman properly, much less two.
For as far as the halacha is concerned, he may not be half a husband to two women, Somehow he had to be a full husband to each of them in all aspects of their relationship.
This was impossible, in the days of Rabbenu Gershon. Today? Fugetaboutit. And hopefully we will not have to make a takana to forbid marriage altogether becomes of man’s silliness.