Dumfries and Galloway and Aberdeen City councils have already given the Convention of Scottish Local Authorities the statutory year's notice to leave and now Glasgow, Inverclyde, Renfrewshire and South Lanarkshire are expected to do likewise.
Glasgow is working on plans for a stripped-down alternative body, with no HQ or permanent staff, which could act for it and other breakaway councils in negotiations with ministers and unions.
The dispute within Cosla, which negotiates funding packages for local government and collective wage deals for around 250,000 council staff, has been simmering for months.
As it runs 16 of the 32 councils, Labour has half the votes in Cosla's prime decision-making body, the monthly leaders' meeting, enabling it to block proposals it doesn't like.
However, Conservative, LibDem, independent and SNP forces in Cosla have started a review of the constitution to dilute Labour's influence.
A key idea is to downgrade the leaders' meeting and elevate the delegates' quarterly convention, where Labour can be out-voted by the other parties.
A Cosla spokesman said: "The organisation will be doing its absolute utmost to ensure that we resolve the issues that have been raised with us."