PERINS School in Alresford is consulting parents over plans to take on more pupils and to alter the criteria for admissions.
The secondary school wants to raise its annual admission number from 208 to 215 with effect from September 2014.
The expansion follows local housebuilding and the number of brothers and sisters from families outside the catchment area wanting to follow their older sibling into the popular school.
Perins also wants to give priority to children of parents employed at the school.
The consultation period runs until January 18. The governors are due to make a decision early in the new year.