Polygamy is allowed by the Torah but outlawed in the countries where Jews live. So, because of Dina dmalchuta dina, Jews cannot have more than one wife. Rabbenu Gershom imposed a ban on polygamy for Ashkenazim, but it is now expired. So my question is: Would a rabbi perform a second wedding for a married man, knowing the marriage would not be recognized by civil authorities, but would by Jewish law? If not, why not?
No. See Shulchan Aruch Even Haezer 1:9, and the Ba'er Heitev 19(ibid).
The Ba'er Heitev explains that since the custom among Jews is to marry only one woman, even without the cherem of R' Gershom, marriage nowadays is based on the premise/condition of monogamy.
Even in a place where polygamy is permitted by law(not that dina d'malchuta dina would matter, in my opinion) and the cherem of R' Gershom didn't apply(for theoretical purposes), it would still be forbidden to take a second wife because she may claim that she only agreed to be married on the condition of being his only wife. Even if she agreed to have a tzara, Rabanim will not and should not perform the marriage ceremony without special circumstances permitting(see below).
Only in certain situations where a woman is not willing to live with her husband, and won't accept a get; is he allowed to take a second wife after deliberation and permission from 100 Rabanim.
Some Jews have taken it upon themselves to be polygamous today. There's apparently an underground movement based on this idea in Israel. I've heard personal accounts and found this article from a Google search that claims these ideas could go all the way up to the Sephardic chief Rabbinate.
But even this article is shrouded in claims and mystery with little hard evidence. Which means it would be hard to be openly polygamous since the social stigmas are very large and real (according to modern social norms adultery is more acceptable than polygamy). So one would probably not be able to legally "register" their second/third/etc wife/marriage in any modern country outside of the Middle East.
Polygyny is permitted the problem is that most people think its not permitted so it is socially not common. Dina Malkuth Dina is mostly irrelevant as Jewish Torah Marriage and Civil Marriage is usually handled as seperate transactions one can easily do just Jewish Torah Keddushin and in fact many marriages are done without civil REGISTRATION. Further since cohabitation and having several woman one has a sexual aspect to their relationship is not illegal in most Western Countries with exception of a few US States it can easily be done without any concern of Dina Malkuth Dina from another interesting point of view is Jurisdiction their is a concept of LAW regarding four corners and if you apply that every Huppa is a seperate private Jurisdiction and therefore it can be claimed in even a WESTERN COURT that it is not even in the GOVERNMENTS appointed LEGAL JURISDICTION.
Further people including Rabbi's have not studied and so don't even understand Rebenu Gershon's decree as he implemented it and as it was exempted during his lifetime and in the period afterwards.
The views of not practicing has more to do with adopting the morals forced upong the Jewish Communities by the surrounding Roman Catholic and other Christian Clergy since the last 1000 years and continues today.
The biggest challenge is not if its Legal by Torah Law but by the fact that very few people are open to the practice which is sad as HaShem who is the master and overseer of all Shiddichim can seen and decide that a women would be a good match for such a man who has a wife but then nobody accepts it because of ignorance and wanting to behave as Monogmist Christians.
I have studied this subject extensively and discussed various aspects of this hundreds of times over the last 1+ years with learned Rabbi's all Sephardim.
Finally I will quote what my Rabbi said " We dont forbid what the Torah Permits." I welcome any questions or queries from those interested in genuine discussion.
And yes if I found the right sephardi woman or women I would ask them to marry me according to the Torah of Mosheh and Yisrael. Shalom Itzik Michael
In those countries where polygamy is illegal, it would be forbidden for a Jewish man to take on multiple wives, based on the principle of dina d'malchusa dina.