Burnham's secondary school hopes to take on more pupils.
Governors at Ormiston Rivers Academy have proposed increasing the yearly intake from 140 to 165 in September 2015.
Principal Joan Costello said the good Ofsted report achieved last September had increased the school’s popularity.
The school is also investing £10.7million in its buildings and is among the top 20 per cent in the country for pupil progress.
It had to turn away about 30 prospective pupils this year due to lack of space, which caused “absolute outcry,” said Ms Costello.
A public consultation on the plans ends on July 18.