The leader of the Scottish Liberal Democrats has urged disillusioned Conservative and Labour politicians to "come and talk to me".
Willie Rennie said he was "full of admiration" for MPs who had already quit the two parties in recent days.
But he said some in Scotland were still to decide whether to do the same.
In his speech to the Scottish Lib Dem conference, he warned them that "to miss this chance today will fill you with regret tomorrow".
Eight Labour MPs and three Conservatives - who are pro-Remain and want another referendum on Brexit - have quit their parties over the past week in order to form the Independent Group in the Commons.
They have cited concerns about the Brexit policies of their respective parties, as well as the "failure" of the Labour leadership to tackle anti-Semitism.
A ninth Labour MP, Ian Austin, has also left the party after accusing leader Jeremy Corbyn of "creating a culture of extremism and intolerance", but says he has no plans to join the new group.
Mr Corbyn has called for Mr Austin to step down as an MP so a by-election can be held.
In his conference speech, Mr Rennie claimed that the Conservatives and Labour are "no longer broad churches but narrow sects".
And he said that his party, which strongly opposes Brexit and wants another referendum, has common ground with politicians from other parties
He added: "Leaving your party after many years is hard. It is a risk. I get that. To those who have taken those first, bold steps I am full of admiration.
"To those in Scotland yet to decide, I say why settle for what you know is not right when you could forge something new that is worth fighting for?
"So, come and talk with me. Let's work together. We have a responsibility to make it happen."
Mr Rennie also claimed that there were "striking parallels between the claims of the Brexiteers and those who argue for independence", with both sides offering "easy slogans, lazy facts, divisive rhetoric and false patriotism".
First minister and SNP leader Nicola Sturgeon has insisted that "independence is not about the isolationism that characterises Brexit" - instead saying it "would see us recognizing and embracing our interdependence with other nations".
UK Liberal Democrat leader Vince Cable also addressed delegates as the two-day conference in Hamilton drew to a close on Saturday afternoon, saying the party had a "bright future".
Deputy leader Jo Swinson spoke at the conference on Friday.