Theresa May is holding meetings with leading Tory Remainers, amid speculation about further defections.
Phillip Lee – who claims the prime minister has ignored the views of pro-EU Tory MPs in favour of Brexiteers – met the PM earlier in Downing Street.
Justine Greening, who says she considered quitting the party and would do so if it allowed a no-deal Brexit, is now in No 10.
Three Conservative MPs quit to join the new Independent Group on Wednesday.
The defectors, like Ms Greening and Mr Lee, back another EU referendum – and they say more Tory and Labour MPs are poised to join their group.
Ex-Tory MP Heidi Allen told ITV’s Peston programme “a third” of Tory MPs were fed up with the party’s direction.
Mr Lee, who quit as a justice minister over Brexit, has been named by Ms Allen as a potential future defector to the Independent Group.
The Right to Vote group, which is chaired by Mr Lee, said he had discussed the campaign’s calls for a pause in the Brexit process and a possible second referendum.
“Talks were open and we are encouraged she listened to our case,” the group said.
Mr Lee has said one of the reasons the Tory MPs had decided to quit the party was the access the Brexiteer European Research Group got to the prime minister, who he said had refused to meet his wing of the party.
Justine Greening – a former education secretary – told the Today programme she had been tempted to break away from the Conservative Party.
“It is something that I have considered, but I have reached a different conclusion for the moment,” Ms Greening told Today.
“I don’t think I would be able to stay part of a party that was simply a Brexit party that had crashed us out of the European Union.”
The Independent Group was set up by eight defecting Labour MPs unhappy about their party’s handling of Brexit and anti-Semitism.
They were later joined by three pro-Remain Tories – who accuse the Conservative leadership of allowing right-wing hardliners to shape the party’s approach to Brexit and other matters.
Labour’s Ian Austin also expressed sympathy with the Independent Group’s aims, saying he would think “long and hard” about his future in the Labour party.
Shadow home Secretary Diane Abbott told BBC Radio 4’s The World at One: “I am very sad that the Labour members of this new independent organisation have gone.
“Up until the last minute, people were talking to them, trying to persuade them not to take the step they have taken.”
She said she hoped they would continue to work with Labour on issues like homelessness, the benefit system, the NHS and “most of all fighting this Tory Brexit”.