Powys council's cabinet wants to replace two schools in Brecon with a new-build English medium secondary and close Llandrindod Wells High School.
Parents, pupils and teachers have protested against the changes, saying there are better options.
The consultation will now end on 1 June.
Councillors will meet to discuss the proposal in Llandrindod Wells on 16 May, with the meeting to be broadcast on the council's website.
A consultation on a proposed shake-up of secondary education in Powys has been extended.