The DUP is supporting a move by Sir Graham Brady to give MPs a say over new national Covid-19 restrictions before they are brought into force.
The SDLP and Alliance have not decided whether they will back the amendment tabled by the chairman of the 1922 Committee of Tory backbenchers.
It comes as the House of Commons considers a six-month renewal of the Coronavirus Act which gave the government powers to respond to the pandemic.
These included moves such as closing down pubs, postponing local elections, and allowing courts to use live links.
Labour, Liberal Democrat and Tory backbenchers are among those supporting Sir Graham's amendment with the signatories including DUP MPs Sammy Wilson and Ian Paisley.
A DUP spokesman said the party's eight MPs would vote for the amendment, increasing pressure on Boris Johnson, who is facing a large parliamentary revolt.
The SDLP's two MPs, Claire Hanna and Colum Eastwood, are still deciding how they will vote, as is Alliance's Stephen Farry.
The North Down MP said: "I strongly support the six-monthly review of the UK Coronavirus legislation. There are a large number of amendments being tabled. I want to see an approach that better facilitates efficient decision-making alongside better democratic accountability and respect for civil liberties.
"So far, I have signed up as a co-sponsor to the Harriet Harman amendment, but have reservations over the Brady amendment. I will be looking at it and the other alternatives over the coming days."
Labour shadow justice secretary David Lammy said his party was "very sympathetic" to the amendment although he has avoided giving clear support.
Ex-Commons Speaker John Bercow and former Tory Brexit Minister Steve Baker are backing the move.
Mr Baker told Sky News: "How do people think that liberty dies? It dies like this with government exercising draconian powers, without parliamentary scrutiny in advance, undermining the rule of law by having a shifting blanket of rules that no-one can understand."
The amendment states that ministers ensure "as far as is reasonably practicable that in the exercise of their powers to tackle the pandemic ... Parliament has an opportunity to debate and to vote upon any secondary legislation with effect in the whole of England or the whole UK before it comes into effect".
Tory ministers on Monday held crisis talks with their own backbenchers in an effort to ward off the revolt over coronavirus laws.
More than 50 Conservative MPs have signalled they could rebel on the matter. That would be enough to wipe out the government's Commons majority if the opposition parties support the Brady amendment.
Health Secretary Matt Hancock, chief whip Mark Spencer and Commons Leader Jacob Rees-Mogg met with the backbenchers in an effort to address their concerns. Mr Baker described it as a "cordial and constructive" meeting.
Mr Hancock told MPs that the government was "looking at further ways to ensure the House can be properly involved in the process in advance where possible".
He said: "I strongly agree with the need for us in this House to have the appropriate level of scrutiny."
But he added that the government had to retain the ability to act quickly where necessary.