Brexit Secretary, Stephen Barclay and senior government officials will discuss alternatives to an Irish backstop.
The Alternative Arrangements Working Group will meet for the first time on Monday after MPs voted to find another way to avoid an Irish hard border.
Home Secretary Sajid Javid has already said that "current technology" could be used.
The Irish PM said the UK was reviewing ideas that had "already been rejected".
Leo Varadkar told RTE that he was "very frustrating" that the UK government "went back to the idea of technology".
The UK is due to leave the EU at 23:00 GMT on Friday 29 March, when the two-year deadline on withdrawal discussions imposed by the Article 50 process ends.
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Who is in the working group?
No. 10 stated that the working group had been established following "substantial support" for the "Compromise Malthouse" as it is called – named after the housing minister Kit Malthouse who encouraged talks between different groups of MPs.
After leaving and remaining engineers the proposal includes extending the transitional period for one year and protecting the rights of EU citizens, rather than using the backstop.
The members of the working group include Conservative MPs Steve Baker, Marcus Fysh, Owen Paterson, Damian Green and Nicky Morgan.
The group will hold regular meetings with Brexit Secretary, Stephen Barclay, as well as officers from HMRC, Office of the Office of Europe and Cabinet No. 10.
Mr Baker, deputy chairman of the Euroscope group, the European Research Group (ERG) warned Sunday that "prime minister" was the "prime minister".
Tweeted: "MPs of Supporters voted to support alternative arrangements in YG but with a wonderful misunderstanding about the whole agreement."
The working group will also hold meetings on Tuesdays and Wednesdays.
By Chris Mason's political correspondent
Death continues. Brexit is just over seven weeks away. So the government is trashing around for a solution.
The government's willingness to provide civil service support by No. 10, HMRC and the Cabinet Office for this Conservative MP group is indicating how seriously Downing Street treats their idea.
But he is still still trying to save the current blueprint, or a variation. The Attorney General, Geoffrey Cox, the government's top lawyer, looks at the legal changes to the backbone that could be requested.
The bottom line is: the government knows she has to return to Brussels with something to ask for. And the First Minister could be back there by the end of the week. So they need to find something, and quickly.
What is the backstop?
By Tom Edgington, BBC Reality Truths
The "backstop" is an "insurance policy" – has planned to avoid a "under every circumstance" hard border between Northern Ireland and the Republic of Ireland.
Under Brexit's contemporary bargain, the border of the 310 miles of Ireland would become the only land border between the EU and the UK.
It's likely that this would mean checks on goods that would cross that, unless both sides could reach a comprehensive trade agreement.
If such an agreement could not be reached, then to avoid those checks and posts on the border or other infrastructure, the backstop comes into force.
He would keep the UK in "single customs territory" with the EU and leave Northern Ireland effectively in the single EU market for goods.
Many MPs are scared that the UK could be "abducted" in this arrangement for many years, allowing him to be unable to discuss his own trade on goods with the rest of the world.
- Read more: Could technology solve the problem of Irish boundaries?
What "alternative arrangements" are there?
Among the alternatives to the backbone that the prime minister said she wants to discuss with EU leaders are:
- "reliable trader" scheme to avoid physical checks on products that flow through the border
- "co-recognition" of EU rules
- "technological" solutions
Mr Javid told BBC Andrew Marr that another "backstop" arrangement could be arranged using "current technology".
He said: "I asked Border Force months ago to advise me to see what other arrangements are possible and have seen it quite clear that you can not have any hard border on the island of Ireland and you can use technology which already exists – that is perfectly possible.
"The only thing missing is a little goodwill on the EU side."
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Attorney General Geoffrey Cox said "leading on another strand of work" – considering whether there was a "hard time limit or an appropriate exit mechanism".
However, Mr. Javid's comments, Sabine Weyand, deputy to the chief editor of Brexit, European Commission, Michel Barnier.
Hi tweeted: "That would not be goodwill but to abolish a duty from public authorities in the EU who have a duty to ensure public health and consumer safety, protect against unfair competition and enforce public policies and agreements international. "