A motion the DUP had backed ahead of a Commons vote later has not been selected for consideration.
The DUP had backed two motions, one asking for the result of the EU referendum in 2016 to be respected and the other was the Malthouse Compromise.
It calls for the Irish border backstop to be replaced with alternative arrangements.
However it was not one of the eight motions chosen for debate by Speaker John Bercow.
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These include proposals such as agreeing to leave on 12 April without a deal, forming a customs union and calling for a confirmatory referendum.
Having voted to seize control of Commons business, MPs are preparing to vote for their preferred Brexit option.
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 had co-signed two motions for consideration at Westminster.
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.
What options are MPs voting on?
The motions selected by Speaker John Bercow are:
- Customs union: This calls for the UK to negotiate a new customs union with the EU immediately after it leaves
- Common Market 2.0: The UK would remain in the single market by rejoining the European Free Trade Association (EFTA) and staying in the European Economic Area (EEA). A “comprehensive customs partnership” would replace the Irish border backstop plan. It would accept continued freedom of movement but with conditions
- EFTA and EEA: The UK would rejoin EFTA and sign up to existing EEA rules and obligations but make them enforceable through the UK courts. Rejects any customs union with the EU, instead seeking agreement on new arrangements for Northern Ireland
- No deal: Agrees to leave the EU on 12 April without a deal
- Another referendum: The public would vote in a confirmatory referendum on any Brexit deal which is passed by Parliament before it is ratified
- Revoke Article 50: If the government has not passed its withdrawal deal, MPs would vote on a no-deal Brexit two days before the UK’s leaving date. If MPs reject no deal, the prime minister would have to cancel Brexit altogether
- Labour’s alternative plan: Negotiate changes to the withdrawal agreement and the political declaration to secure Labour’s position, and pass these objectives into law
- Contingent preferential arrangements: The UK makes its budgetary contributions to the EU to the end of 2020 and agrees with the EU a period of two years in which UK goods have full access to the EU
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.
Brexit: DUP-backed motion not up for Commons vote}