The DUP has backed two motions ahead of a Commons vote later, when MPs take control of parliamentary business to try to break the Brexit deadlock.
One asks for the result of the EU referendum in 2016 to be respected.
Another is the Malthouse Compromise, which calls for the Irish border backstop to be replaced with alternative arrangements.
Having voted to seize control of Commons business, MPs are preparing to vote for their preferred Brexit option.
Speaker John Bercow will decide which of the 16 motions MPs have tabled will get chosen for debate.
He will select around half a dozen options, likely to range from cancelling Brexit to leaving the EU without a deal, with MPs marking on paper each option with a “yes” or “no”.
The process is likely to continue in to next week. However, it is unclear whether MPs will be free to vote as they wish or will take orders from party leaders.
There have been suggestions that Theresa May must name the date she will step down to have any hope of winning MPs’ approval for her deal at the third attempt.
DUP deputy leader Nigel Dodds has co-signed two motions.
The party previously backed the Malthouse Compromise, which would see Mrs May’s withdrawal deal remain but without the backstop, which would be replaced by alternative arrangements.
Another referendum: The public would vote in a confirmatory referendum on any Brexit deal which is passed by Parliament before it is ratified.
Meanwhile, leading Brexiteer Jacob Rees-Mogg has said he will only back the government’s Brexit deal if the DUP does.
On Tuesday, he had hinted he could back the prime minister’s plan, at the risk of there not being any Brexit at all.
But in a piece for the Daily Mail, he said his support is conditional on the DUP’s decision.
So far, the DUP has not indicated that it is prepared to back the government’s deal unless there are changes to the Irish border backstop.
On Tuesday, Sammy Wilson, the party’s Brexit spokesperson, said a long delay of up to a year would be preferable to the deal.
But the DUP said its position as a whole remains unchanged.