Gresham's School backers say they urgently need more time to submit supermarket and other plans for a site close to Holt Market Place, which they claim are vital to safeguarding the school's future.
They are asking planners to delay deciding a rival store bid until May, when the Gresham's application is expected to be ready.
A governor has said the viability of the independent school, which has been a north Norfolk institution since 1555, could be in doubt if it was not able to keep pace in a highly competitive market by providing new facilities, funded by the store and associated development.
Adel MacNicol was speaking at Friday and Saturday's public consultation exhibition on Gresham's ideas for developing its Grade II-listed pre-preparatory Old School House and surroundings.
Gresham's needs to generate £10m through the development to fund a new sixth form centre and pre-preparatory school.
But Gresham's is in a head-to-head battle with Holt business Thaxters which has already submitted plans for a supermarket on the site of its Hempstead Road headquarters.
Tim Holmes, director of Cambridge-based Endurance Estates, Gresham's development partner, said there was only room for one more supermarket in Holt as well as the existing Budgens store.
'If Thaxters get their permission it would mean that our proposals for a supermarket would be unviable,' said Mr Holmes.
'Our plea to the planning committee is: 'give us the chance to come forward with our scheme so that it can be considered alongside Thaxters, each on its merits.'
'We believe our scheme is sequentially better.
'It is closer to the town centre and would encourage more people to visit other shops.''
Mrs MacNicol, the Gresham's governor overseeing the development plan, said the school, Holt's biggest employer, had already fallen behind its competitors in building new facilities and urgently needed to raise cash from its un-needed assets to underpin the school's future.
'If we were not able to raise any money I would seriously question the viability of the school into the future – and that's not just scaremongering,' said Mrs MacNicol.
'We have always been a forward-thinking school – we wouldn't be here in the future if we didn't continue that tradition.'
At the exhibition, attended by more than 200 people, Gresham's asked the public's views on 'emerging ideas' for a 10,000sq ft supermarket – roughly the same as Thaxters' – with flats above, behind the 1858 Old School House, which would be kept and developed into ground-floor retail with flats over.
The proposals would see the loss of about six parking slots on Church Street and Station Road, replaced with 150 spaces off Station Road, along the edge of the current playing field. HGV deliveries would be time-controlled to avoid congestion.
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