A group of four crossbench senators announced they would oppose the move, arguing government legislation went too far.
Instead, they called for an industry review of not-for-profit fund governance.
The senators also want the review to consider how industry funds could increase their investment in Australia.
The government needs six of the eight crossbench votes to have its legislation clear the Senate against Labor and Greens’ opposition.
The senators – Glenn Lazarus, Jacqui Lambie, John Madigan and Nick Xenophon – said forcing not-for-profit industry funds to implement new governance arrangements would impose additional administrative costs and other burdens.
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