Former pro-EU Prime Minister John Major said last week this may be Johnson's preferred route.
The anti-Brexit campaigners filed two linked challenges to Johnson in Scotland's Outer House of the Court of Session in Edinburgh and the court's Inner House, the highest Scottish court.
"We're bringing this case because we're dealing with a British Prime Minister who brags about not obeying the law and has form for doing things that are unlawful".
Many expect the issue to ultimately end up in the UK Supreme Court.
There is no clear consensus among the parliamentarians about who might succeed Johnson should he be forced from the Prime Minister's office.
The legal action - led by businessman Vince Dale, SNP MP Joanna Cherry QC and Jolyon Maugham QC - is asking the court to require Johnson to seek an extension to avoid leaving the European Union without a deal.
A panel of judges will then also seek to establish what might happen if the prime minister refuses to act, including whether the court could use its "nobile officium" power to effectively sign a letter to European leaders.
Boris Johnsons new Brexit proposal has gotten such a chilly reception in Europe that some people think it must have been created to be rejected: Johnson is less interested in getting a deal, on this theory, than in deflecting blame for the inevitable breakdown.
The Prime Minister's Europe adviser, David Frost, has been in Brussels for technical talks with officials.
If the British prime minister does not change his position on Britain's departure from the European Union there will be no Brexit deal, Ireland's foreign minister said on Friday.
He also expressed concern over Boris Johnson's suggestion that the now defunct Stormont Assembly be given a vote both on whether to opt into the all-island regulatory system in 2021, and whether to remain in it after an initial four-year period.
A United Kingdom spokesman said: "We have made a significant offer this week". Tusk spoke out after a 20-minute call with Irish Premier Leo Varadkar.
Much of what happens in the three-year saga now depends on whether Brussels agrees to open formal talks on the brand new Brexit plan Johnson unveiled Wednesday.
Pincher called the new proposal "a good, fair and reasonable compromise" that presents a "broad landing zone" for talks that would enable the U.K.to leave the bloc in an "orderly and friendly way".
European Commission president Jean-Claude Juncker spoke to Mr Varadkar and emphasised that "stable and predictable" measures were needed that "cannot be based on untried arrangements" that would be left to negotiations in a transition period. "It's a no deal budget so it has to be more conservative than previous budgets and what that means is no across the board income tax cuts and no across the board welfare increases", he said.
A spokesman for Downing Street told POLITICO that "The PM has said that what we want to do is get a deal, and get Brexit done on October 31st without any further pointless delay".
But he accepted that they are "some way from a resolution" on the situation.