They know it's illegal in Australia but even so, two senior Islamic leaders say it's happening in their community and the Government shouldn't turn its back on those who choose to do it.
Speaker: Keysar Trad, Islamic Friendship Association president; Hanefa Trad; Sheikh Khalil Chami, Islamic Welfare Centre in Lakemba
ALISON CALDWELL: Keysar Trad is the president of the Islamic Friendship Association of Australia.
He's also known as the man who used to represent the controversial former Mufti of Australia Sheikh Taj el-Din al-Hilaly.
Keysar Trad supports polygamous marriages.
He says it's time Australia recognised them, in order to protect the rights of women.
KEYSAR TRAD: We, as a society, should say okay well if this woman has wilfully chosen to enter into this relationship, make a lifelong commitment to this person, to be married. It shouldn't matter.
If it was a business and the business had four partners, we'd recognise that. But why don't we recognise it when it comes to consensual relationships amongst adults.
ALISON CALDWELL: Speaking to Triple J's Hack program, Keysar Trad revealed that he once proposed to another woman with the consent of his wife, Hanefa.
KEYSAR TRAD: I certainly would not have entertained the thought of having a relationship without a religious marriage. Rather than entertain any thoughts of an affair, I thought the only decent thing to do was consider a proper commitment to that person.
ALISON CALDWELL: Hanefa Trad was asked if it was just about men wanting sex with more women.
HANEFA TRAD: Yes, it can be. But having it in the right way but doesn't happen it in like go to prostitute or just date and just go for a woman for one night and leave her.
ALISON CALDWELL: Bigamy and polygamy are illegal in Australia.
In the Islamic community, people get around the laws by marrying in religious ceremonies performed by Sheikhs.
KHALIL CHAMI: Polygamy in Islam is allowed. I know person who have three wives. Not one, not two.
ALISON CALDWELL: Sheikh Khalil Chami is with the Islamic Welfare Centre in Lakemba. He says he gets asked to conduct such ceremonies almost weekly but declines.
KHALIL CHAMI: There is a lot of sheiks here without any qualification, without any place, without any. They'll conduct their marriage, no problem at all.
ALISON CALDWELL: He says the Federal Government should register polygamous marriages.
KHALIL CHAMI: And especially with the Attorney-General which is really, we can start something - not in the capacity open the door for all this thing. So I think, if it has been allowed in a way, everyone will have control over this thing.
ALISON CALDWELL: The Attorney-General Robert McClelland wasn't available for an interview. Instead his spokesman issued a statement saying:
(Extract from Attorney-General's statement)
Under Australian law, marriage is defined as the union of a man and a woman to the exclusion of all others. Polygamous marriage necessarily offends this definition. The Government is not considering amending this definition, or in any way recognising polygamous marriage.
(End of Extract)
ALISON CALDWELL: Undeterred Keysar Trad says he's hoping to find another wife to join his family, to do so, he says, would be to honour his first wife.