The emerging Greater Exeter Strategic Plan (GESP) is intended to cover the East Devon, Exeter, Mid Devon and Teignbridge Council areas.
According to the Greater Exeter Strategic Plan website, reports were due to be considered by committees at the four local authority committees throughout July to consider whether to begin a further round of consultation on the document.
"The meetings will ask councillors to agree the 'draft policies and site options' document and a public consultation to begin in September", the website said.
It added: "Exeter City Council will be first to decide at their executive meeting on 7th July, followed by Teignbridge on 21st July, East Devon on 23rd July and Mid-Devon on 6th August".
The draft policies and site option document said that the "Greater Exeter councils will target the delivery of 2,663 homes per year in the Greater Exeter area (53,260 total) between 2020 and 2040".
Exeter and Teignbridge councils had both agreed to progress the document.
A report to East Devon District Council's strategic planning committee had recommended that the proposals proceed to the next round of consultation.
The report said that "how growth is accommodated and how this is coordinated between the authorities will be key moving forwards as will the need to coordinate the delivery of infrastructure to support the development that is needed".
But the committee voted instead in favour of a motion recommending that the council withdraw from the plan-making process.
According to local press reports, members expressed concerns about the emerging plan, with one councillor saying it was "all about volume house building, is dangerously flawed and contradictory".
The committee's recommendation will now be considered at a full council meeting.
A spokesperson for East Devon Council said: "On the assumption that the full council endorses this recommendation then the continuation of GESP will be for Exeter City Council, Teignbridge District Council and Mid Devon District Council to decide.
"East Devon District Council will consequently focus on preparing a new local plan for the district but will respect the legal duty to cooperate with its neighbouring areas."
East Devon Council is led by the independent Democratic Alliance Group in coalition with other independent members.
The GESP team was contacted for comment but it had yet to respond by time of publication.
Preparation of the plan had previously been delayed by almost a year and a half after work was suspended to take into account changes in political administrations across Devon.
In September 2018, a previous consultation on the GESP was delayed after East Devon councillors refused to endorse a draft of the plan.
Another joint strategic plan covering the Bristol city region fell apart after it failed at examination last year.