Tax havens under UK jurisdiction could be forced to be more open about who owns assets held there if a group of MPs get their way next week.
A group led by Tory MP Andrew Mitchell and Labour's Margaret Hodge want UK overseas territories (OTs) to introduce a beneficial ownership register.
This, they hope, will shine a light on money laundering and the proceeds of people trafficking and other crimes.
The UK created its own publicly accessible register in 2016.
But the government failed in its efforts to persuade many overseas territories to follow suit.
More than 40 MPs have signed an amendment to the Financial Services Bill requiring the UK to help all overseas territories and Crown dependencies set up a publicly accessible register of the beneficial ownership of companies within their jurisdictions.
If passed, it would oblige them to do so by the end of 2020.
MPs backing the move include former Tory Cabinet ministers Ken Clarke, David Davis and Sir Oliver Letwin, senior Labour backbenchers Margaret Beckett and Ed Miliband and deputy Lib Dem leader Jo Swinson.
Ian Blackford, who leads the SNP group in Westminster and Green Party MP Caroline Lucas, have also put their name to the amendment.
Mr Mitchell and Ms Hodge have long campaigned for more transparency over who owns assets in the UK and its dependencies to ensure "dirty money" cannot be laundered into the UK economy, having sought to pass legislation last year.
The BBC's parliamentary correspondent Mark D'Arcy said the overseas territories and Crown dependencies remain strongly opposed to being compelled to act.
But he said the weight of support behind the amendment meant the government might be unable to resist it, at a time when it has suffered a string of Commons defeats over Brexit.
Ministers say they have made progress in recent years. Since 2016, UK law enforcement agencies have had real-time access to information on companies incorporated in such territories.
The UK says it is committed to "influencing" overseas territories and Crown dependencies when it comes to beneficial ownership registers, with the aim of them becoming the global standard by 2023.