If it passes its fate will then be decided in the House of Representatives.
All MPs and senators have a conscience vote.
Early Tuesday night senators agreed to increase prison terms for people who break new laws which extend stem cell research.
While the laws have not yet passed the parliament, if they do, there will be harsher uniform prison terms for people who abuse the process.
Anyone offering some sort of reward for a human egg, sperm or embryo now faces 15 years in prison under the laws.
This also applies to placing a human embryo in an animal, as well as fertilising an embryo outside a woman's body, for a purpose other than to achieve a pregnancy.
Changes sought by Greens senator Kerry Nettle including the setting up of a national stem cell bank, were defeated.
Emotional debate
On Tuesday senators voted 34 to 31 in support of the legislation before moving to discussion of proposed amendments.
It's followed an emotive and intense debate in the upper house Monday night and Tuesday morning which has shown politicians are fairly evenly divided on the issue.
Senator Patterson's bill would allow researchers to clone human embryos to extract their stem cells in the hope of one day finding cures for debilitating diseases.
Existing laws allow stem cells to be harvested from surplus IVF embryos but prevent them being cloned.
Liberal senator Julian McGauran has warned of an horrific future peopled with bizarre human-animal mongrels.
But Democrats senator Andrew Murray says he has no fears about the emergence of Frankenstein-like monsters.
And Ageing Minister Santo Santoro says there's simply not enough evidence that stem cells from cloned human embryos would produce the expected medical breakthroughs.
Debate on Senator Patterson's bill and possible amendments continues in the upper house this afternoon.
After a final conscience vote in the Senate the legislation will move to the House of Representatives.