Originally designed for 1200 students, the building was extended last year to take its capacity to 1625.
However, the school’s roll has already reached 1436, and board chairman Adrian Januszkiewicz said the school was likely to "reach our current capacity by or about 2027".
Mr Januszkiewicz said ministry plans to buy land for a second Queenstown high school had not progressed.
"As far as we know, no land has been acquired for that purpose, so it seems unlikely this can be a realistic solution for the foreseeable future.
"So we’ve said to the ministry, well, given land acquisition, planning, etc, takes up to 10 years — well, it took 10 years for this school, [but even] seven or eight years — we have an immediate issue to address.
"We have tabled to the ministry that the current site could be enhanced/expanded to accommodate up to 2000 students for a fraction of the cost of building a new school.
"From the school’s perspective, it is a workable solution and is supported by the board.
"And for the taxpayer it seems to us it would represent the most efficient use of public funds."
Mr Januszkiewicz said the school was "currently in a great position, with world-class facilities and everything we need to provide an amazing educational experience for our students and our community".
However, "our desire is to try to avoid any last-minute scramble when capacity issues do eventually arise".
"[The issue] needs to be addressed, and if we don’t address it in a measured and planned way, then we’re going to have emergency classrooms thrust upon us, and we’re going to have to deal with those [students] anyway."
He appreciated the ministry had "a whole bunch of priorities they need to sort of juggle".
Discussing the issue was taking place "in an educational sector environment which is facing significant budget constraints and complex fiscal challenges, so it is not proving to be a straightforward discussion".
Mr Januszkiewicz said the board was meeting with the ministry soon.
"Hopefully we’ll get more clarity around [a second extension], but it feels like they’re more open to that than they might have been in the past, so we’re taking that as a positive."
Ministry of Education leader south Nancy Bell said the department was working with the school to manage growth beyond its capacity of 1625, but "no decisions have been confirmed yet".
