Advice from the Ministry of Education had been that its out-of-zone students would provide a buffer, but board chair Gerald Young said that accounted for only 60 pupils.
He said the school had to build more classrooms - there are plans for a five-storey science and technology block - or shrink the zone.
"We are faced with a dilemma," Dr Young said. "Soon we won't be able to take any more, but we haven't got the funding and we can't put up buildings overnight.
"I would not like to be the chairman and go out to the community and say we are going to shift the zone. I would get hung for that. Or shot. But if we can't get traction on new buildings then [the] board would have to face that decision."
INTERACTIVE MAP:
Auckland Grammar's headmaster Tim O'Connor said it was actively working with the ministry, including talks about the development of new schools.
"We have 2500 on the roll, that's at capacity. And we don't want to be any bigger than we are," Mr O'Connor said. "But there's no silver bullet. We have to be aware of demand and everyone understands that."
The school wanted to be able to enforce its existing zone more strictly. It battles to ensure its students are truly local - some give fake addresses or buy temporary properties to qualify for enrolment.
Auckland councillor Christine Fletcher said she believed there was a strong need for another school and it was short-sighted not to have land-banked a site. "It is unfair to have continued pressure on families and schools; we need to invest before it turns to chaos," she said. "It is reaching the point of a showdown."
Act's Epsom MP David Seymour said he was opposed to zone shifts - he headed a campaign when two nearby schools proposed overlapping their zones into the area last year - and to intensification.
One idea was to make a rule so that students in new houses would not be included in the zone, he said. There was a need to balance the needs of people who lived in Epsom with the "interests of developers who want to develop property and sell an education with that property".
The Ministry of Education's Katrina Casey said it was monitoring population and growth, particularly in areas where it knew school-age populations were rising.
"Both schools are managing their rolls well and we are always available to help find a solution that best meets the needs of individual schools and the wider network where required."
Ms Casey said many of the apartments being built in the Auckland CBD were small.
"Experience tells us apartment blocks aren't always as popular with families with school-age children as, say, more traditional homes, but over time that may change."
The Government was spending $350 million expanding schools and building new ones across Auckland over the next four years.
In the next 18 months it would build more than 230 classrooms. Nine new schools were expected by 2020, with two announced for Kumeu and Scott's Point.
Zoned out
What's the problem?
Auckland Grammar School and Epsom Girls' are at capacity, and concerned about rapid population rise within their zones.
What is a zone?
The zone is the area from which students are guaranteed entry to the school. Due to the popularity of Auckland Grammar and Epsom Girls', they have a large effect on property prices, adding up to 30 per cent in value.
What could be done?
More classrooms on the existing space, smaller zones, or new schools. Potential sites include the old College of Education site in Mt Eden.
