There are now 25 schools under investigation over an alleged hardline Muslim plot to force out governors and headteachers.
Birmingham City Council said it was appointing a new chief adviser to directly handle at least 200 complaints received in relation to the Operation Trojan Horse allegations focusing on schools in the city, as the investigation continues to widen.
The council's investigation, running in parallel to a separate inquiry by the Department for Education (DfE), is due to initially report back in May.
However, Sir Albert Bore the council leader expressed "frustration" with the two-tier schools system which means academies - which are at the heart of the allegations - are outside the local authority's control, because they report directly to the DfE.
The council said Ian Kershaw, managing director of Northern Education, will take up the chief adviser role, and it is also setting up a review group of MPs, councillors, national teaching and governors groups, the police, and faith leaders, to look into the claims.
Mr Kershaw will publish his findings to the review group, which will then report to a council committee.
Sir Albert said a follow-up report containing recommendations for schools locally, and for the DfE to look at nationally, would be published by July.
He also confirmed the council had spoken to the local authorities in both Manchester and Bradford, during its three-month long investigation, where similar allegations have been raised.
Separately, Education Secretary Michael Gove has personally sent Ofsted in to inspect 15 Birmingham schools in recent weeks, after the allegations first broke.
Concerns over how some of the city's 430 schools were being run first emerged when an anonymous letter known as Operation Trojan Horse was leaked, claiming a small but radical group of Muslims were pursuing their own agenda in the classrooms, with uncooperative headteachers and governors forced out.
The unsigned and undated document also claimed to have caused "a great amount of organised disruption" in the city, crediting the plan with forcing a change of leadership at four schools.
Since the letter came to light, anonymous whistle-blowers have claimed that boys and girls were segregated in classrooms and assemblies, sex education was banned, non-Muslim staff bullied, and in one case it was alleged that the teachings of a firebrand al Qaida-linked Muslim preacher praised to pupils.
Sir Albert said the council was "in dialogue" with the DfE, and confirmed none of the Ofsted inspection reports would be published by the education watchdog until after Easter.
West Midlands Police is also still looking into the authorship of the document, the council's leader said.
Sir Albert also described as "frustrating in the extreme" the situation whereby the city council is investigating possible wrong-doing at academies, where it has only limited powers to intervene if evidence of wrong-doing is uncovered.
Instead, the council has been speaking with headteachers and governors of non-local authority schools voluntarily and making approaches on the basis of its legal duty of care towards children.
He said: "It (the allegations) started off with reference to academy schools and that for us was a bit of a problem because academy schools are of course accountable to the DfE, not to ourselves."
Sir Albert added: "It's in the DfE's interest to settle some matters with us so we can move forward - it's unsatisfactory that you don't know who's on the governing body of academy schools."
The council's education chiefs have said that pupils deserve a "fantastic education system" while teachers "deserve to be able to work in their jobs without intimidation".
The allegations detailed in the Trojan Horse letter focus on the Park View Educational Trust, which runs three schools in the city - all of which have been subjected to snap Ofsted inspections in recent weeks.
Among further claims which have since come to light, one former anonymous staff member at Park View Academy in Alum Rock alleged a colleague had in an assembly praised the firebrand al-Qaida-linked Muslim cleric Anwar al-Awlaki - he was killed by a US drone strike in Yemen in 2011.
The school trustees have firmly denied all the claims, branding the allegations "a witch-hunt", while pointing to very good academic results among its pupils.
All of the city's MPs recently wrote a letter to Mr Gove calling for a full inquiry into the issues to settle the matter.
A DfE spokesperson said its investigation was continuing and it would be inappropriate to comment further.
Meanwhile, Deputy Prime Minister Nick Clegg said schools should not be allowed to become "silos of segregation", as he backed the DfE's probe.
At a press conference in Westminster he said: "I am very concerned whenever I hear allegations that schools, funded by the taxpayer, become vehicles for the propagation of particular ideologies which divide young children and pupils off from other people in society.
He added: "The best faith schools, partly because they are conscious of their own faith, reach out to other faiths, reach out to other schools in the local community, teach about other faiths, rather than allowing them to become silos of segregations."
He said his comments were not "directed at any one faith", but said schools which "turn inwards" needed to be investigated.