The DUP, SDLP and Alliance are among Westminster parties seeking to amend a proposed government bill that aims to override part of the Brexit deal.
MPs will hold the first substantive debate on the Internal Market Bill on Monday.
Downing Street claims it is a safety net, in case talks to work out details of the Northern Ireland Protocol fail.
The EU said if Parliament passes the legislation, it will be difficult for trade deal negotiations to continue.
Northern Ireland’s political parties are divided over the bill, which the government has admitted would break international law.
Some unionist parties gave it a broad welcome, saying the EU cannot be allowed to impose an economic border between Northern Ireland and the rest of the UK.
The Ulster Unionists do not support the protocol, but said the government should not be threatening to break international law to “right a terrible wrong”.
But Sinn Féin, the SDLP, Alliance and the Greens criticised the British government for reneging on previous commitments.
The bill would give UK ministers the power to reduce the amount of paperwork that Northern Ireland firms have to fill in on goods bound for Great Britain, such as export and exit declarations, or to remove the need for them entirely.
It would also allow the UK to narrow the scope of EU state aid rules in Northern Ireland.
It is controversial because it would change the terms of the Northern Ireland Protocol, a crucial part of the legally-binding Withdrawal Agreement agreed by both sides prior to the UK’s exit from the EU.
What is the Northern Ireland Protocol?
The Northern Ireland Protocol is designed to prevent a hard border in Ireland – or even any new checks at the Irish border.
It does this by effectively keeping Northern Ireland in the EU’s single market for goods.
This will mean products entering Northern Ireland from the rest of the UK will be subject to new checks and control – the so-called Irish Sea border.
However, the precise nature of these checks needs to be agreed by the EU and UK and are being negotiated in parallel with the trade talks, which Prime Minister Boris Johnson wants concluded by the next European Council meeting on 15 October.
It will also mean when relevant EU laws are amended or new ones are drawn up, they will also apply in Northern Ireland.
This bill has already been the subject of much public debate, but now the parliamentary drama ramps up.
Downing Street maintains the legislation is a safety net, in case talks to iron out details of the Northern Ireland Protocol fail.
But the SDLP and Alliance, who oppose what Number 10 is doing, are supporting amendments to try and block the bill from proceeding through Parliament.
Boris Johnson, however, has a large majority – so even if some in the Conservative Party vote against the legislation, he’s likely to secure the support of the DUP, who welcomed the bill but said it’s not the finished product.
Today is only the first hurdle for the bill, as the government attempts to fast-track it into law.
‘Undermining devolved institutions’
Downing Street wants to fast-track the bill’s passage through Parliament, but the SDLP is one of several parties to table an amendment aiming to block it from proceeding.
It calls the legislation a “self-described breach of international law… and an outright violation of the Good Friday Agreement, including by undermining the power of devolved institutions”.
The SDLP leader, Foyle MP Colum Eastwood, said the bill “brings us closer to a hard border in Ireland than we have been at any point in these negotiations”.
His party colleague Claire Hanna told the BBC’s Good Morning Ulster programme that goods checks would be easier to manage at ports than along the land border.
“I deeply regret there being any barriers to trade,” the South Belfast MP said.
She added that both the SDLP and Alliance “pointed out the flaws” in last year’s EU Withdrawal Agreement Bill and the trade barriers it created between Northern Ireland and Great Britain.
“But the simple fact of the matter is, you can more easily monitor trade going through a finite number of ports than you can going through 270 crossings or whatever we have on the border,” she added.
Ulster Unionist leader Steve Aiken told the same programme that despite problems with the Northern Ireland Protocol, his party does not agree with the government’s legislative approach.
“The United Kingdom cannot be seen to be repudiating an international treaty because where does that leave all the other international treaties, including the Belfast Agreement?” Mr Aiken said.
Alliance is backing a cross-party blocking amendment, signed by the SNP, Plaid Cymru, Liberal Democrats and the SDLP.
‘Not the finished product’
The DUP supports the legislation, but has also submitted amendments that aim to address the concerns it still has over parts of the Brexit deal.
The party’s chief whip in Westminster, Sammy Wilson, said the bill was a massive step forward for business in Northern Ireland – but “not the finished product”.
One amendment seeks to ensure the UK would set the rules on state aid in Northern Ireland, after the end of the transition period.
State aid concerns the type and amount of government support that can be given to businesses.
As businesses in Northern Ireland will still be in the EU single market after 31 December, they would be covered by EU rules.
Great Britain-based businesses which trade in Northern Ireland could also be covered by these rules, something the UK government wants to prevent.
Mr Wilson told the BBC’s Good Morning Ulster programme that last year’s deal was “one-sided” in favour of the EU in terms of state aid.
“The Withdrawal Agreement allows the EU to insist on examining any state aid policies which the UK government applies to the whole of the United Kingdom,” the DUP MP said.
“But it does not allow, and there is no mechanism by which the UK government can block or object to state aid policies within the EU.
“So we can have a situation where the Irish government subsidies and supports industries in the Republic, which would be to the detriment of Northern Ireland, and we would not have the ability either to stop them doing so or indeed to give the same kind of support to our industries in Northern Ireland without the agreement of the EU.”
The first debate on the bill will get under way on Monday afternoon, and it will be up to the Commons Speaker to decide whether any amendments are selected.