The Opposition opposes same-sex marriage, while the Greens' policy advocates marriage for all, regardless of sexuality or gender identity.
Public opinion is divided. The most recent Galaxy poll put support at 50 per cent. Last night, the polyamorists' case was put by the Glasbys. Marc and Belle had been married and happily monogamous for more than 30 years until Dorothy, who had been separated from her sister at birth, entered the picture.
The three have been in love since. Glasby spends alternate nights with the sisters, after some hiccups working out jealousy issues.
"Until the poly relationship I am now involved in, I was completely faithful to my wife for the 30 years that we have been together," he said.
"If we had not met her sister, and if the unique set of circumstances that we found had not been present, then I would have continued to be a happy, faithful, monogamous husband until the day I died."
Glasby said that while some used the term to describe "swinging" lifestyles, truly polyamorous people needed to clearly differentiate between short-term sexual adventures and long-term committed relationships.
"The whole experience has been amazing," he said. "It was not something we ever expected to happen in our lives, but it has, and day by day we are finding better ways to deal with any problems that arise."
But Glasby said it was unfortunate he lived in a society that did not tolerate "multiple marriages" and in which polyamorists could lose friends and face discrimination if they declared their relationships.
"If I had the option, I would most certainly be legally married to both women, as they are both in every respect, except on paper, my wives."
Appearing with the Glasbys was Aboriginal elder Witiyana Marika, a founding member of indigenous rock group Yothu Yindi, who has two wives, says Aboriginal culture supports multiple wives, and argues it strengthens families.
Lebanese Muslim Fatimah Youssef also claimed benefits for women from polygamy, allowed because God knew that "man was weak".
Sierra Leonean Tony Kamara, whose father had two wives and who said polygamy was a normal part of life for the community in Australia, enjoyed his large family but recalled jealousy and fear between the wives.
And psychologist and community worker Eman Sharobeem said religion could subjugate women into accepting polygamous relationships that drove some "to the point of mental health breakdowns".
Polyamory Australia, one of a number of advocacy and networking websites, claims its community is diverse and growing, with several hundred attending regular meetings, discussion groups and other events, and using online forums.
"We could be rural, inner-city urban or suburban, straight or gay, bi- or asexual ... agnostic, atheist, Christian, wiccan, Buddhist, pagan or Mormon ... dressed as daggy geeks [or] fetish fashionistas ... but our common goal is that of ethical, multiple, intimate relationships and respect for our incredible, wonderful, stimulating diversity," the site says.
Polyamorists and gays have agreed to more open dialogue following a dispute over their "A Brighter Future for All Kinds of Love" float in this year's Gay and Lesbian Mardi Gras, eventually settled amicably.
But swinging wider public support their way will be harder.
The Greens have been accused of hypocrisy - even by Christian lobbyists opposing gay unions - for supporting same-sex marriage while denying polyamorists the same right.
And just getting gay marriage accepted will tough enough. During the parliamentary hearings the proposal was rejected by all religious groups except Buddhists and the Union for Progressive Judaism, political support is uncertain, and many Australians remain unconvinced.
