The Professional Cricketers' Association is willing to support two overseas players per county side in order to accommodate the Kolpak signings, which will cease to exist by the end of 2020.
Britain's withdrawal from the European Union was finalised last month and its effects encompass the invalidation of Kolpak contracts beyond December.
The Kolpak ruling was handed down in 2003 and has been primarily used by South African cricketers. It basically allowed citizens of countries that have signed European Union Association Agreements, including those belonging to Caribbean nations, South Africa and Zimbabwe, the right of free movement as EU citizens.
Kolpak contracts permitted players to represent a county club as a local recruit provided they did not play international cricket.
Some of the high-profile players who benefitted from the Kolpak loophole are Simon Harmer, Duanne Olivier, Kyle Abbott and Morne Morkel - all of whom have played Test cricket for South Africa.
Brexit, however, entails a knock-on effect on Kolpak deals, reclassifying the non-overseas signings as foreign players following the end of the 2020 season.
Overseas players holding British passports will continue to have their rights to play as a "local cricketer" protected past 2020.
The PCA has thus backed the England and Wales Cricket Board's suggestion to increase the overseas quota from one to two cricketers in the County Championship, One-Day Cup and T20 Blast.
"We are very aware of the sensitive issues that Brexit has been causing a number of PCA members for over three years," said PCA chairman Daryl Mitchell.
"A number of Kolpak-registered players have committed to a career in England beyond 2020 and their needs as PCA members are very important to us," he added.
"Our view is increasing overseas players to two per county in the County Championship and One-Day Cup would be a positive outcome."
The inaugural edition of the Hundred competition will see a maximum of three overseas players per team.
The change of criteria for Kolpak registrations is expected to reduce the talent drain from South Africa, an issue highlighted as a major factor explaining the country's decline in cricket.