A letter from an Essex headteacher to local colleagues reveals that 31 secondary schools in the county have expressed an interest in a possible partnership with Serco, a support services company, following initial talks.
Although heads could not "sack" the LEA, the partnership would enable them to buy advice on areas such as financial management and information technology from Serco.
"There is general agreement at ASHE Council (the umbrella group of Essex secondary heads) that at a strategic level, Essex LEA is in disarray," says the letter.
Serco, which already has contracts running LEAs in Bradford and Walsall, was one of three companies shortlisted under controversial plans that would have meant Essex voluntarily contracting out its education services.
The plan was dropped late last year leaving heads concerned that the education authority would be left in limbo following the retirement of its former director Paul Lincoln.
It has since emerged that Mr Lincoln went on to work for the US company, Edison. Edison has been in separate talks with Essex LEA about providing a trial support package for up to 15 schools this autumn.
The TES has learned that only five schools had signed up and that the deal was put on hold earlier this month while the authority conducted an internal investigation into "issues of propriety".
Edison announced at the end of April that Mr Lincoln had lost his seat on its board of directors, although he would remain in an "ex officio capacity".
Councillor Paul Sztumpf, leader of the Labour opposition on Essex Council said he was appalled that the heads' confidence in the LEA was so low they were making their own deals.
An Essex County Council decision on the possible Edison deal is expected in the near future. It is aware of the heads' talks with Serco.