Unison and the GMB, the unions that represent assistants, have asked the TUC to begin formal proceedings against the Association of Teachers and Lecturers for poaching members.
The number of support staff has grown dramatically from 136,000 in 1997 to 225,000 this year and will rise further as the deal to cut teachers'
workload is introduced in September.
TUC rules forbid unions from recruiting in areas already served by other unions.
If the TUC finds the ATL has breached these rules then the union will be ordered to end the practice or face sanctions that could ultimately include expulsion from the TUC.
Christina McAnea, Unison's education policy officer, said: "We have reached the point where we have to take a stand. We need to ensure support staff are represented by a union which can do business on their behalf. Unison does not try to represent teachers because we do not have the expertise."
Dr Mary Bousted, general secretary of the ATL, said she was confident the association would reach agreement with support staff unions over who it could represent in the future.
"Professional roles within education are changing and the new professionals will need support. It remains to be seen how their interests will be best served in the future," she said.
A TUC spokesman said it was working to achieve agreement between the parties and hoped the matter could be resolved amicably.
The ATL is also at loggerheads with the National Union of Teachers. Gerald Imison, ATL deputy general secretary, has said it will refuse to participate in talks with the union on the workload deal, which the NUT has not signed.