Police are looking into claims sexual offences were carried out at the national school for deaf children.
Donaldson's School in Linlithgow has been given a week to come up with a plan to deal with serious concerns about the way the school is being run.
Police are also assessing allegations. It is understood they relate to claims of serious sexual offences and how some people at the school responded to them.
The school said it was unable to comment at this time.
A spokesperson said: "This is a sensitive matter and with internal investigations ongoing, we are unable to comment on the names, job titles or any other specifics of this case".
BBC Scotland understands some allegations are historical in nature.Insufficient progress
Donaldson's is a grant-aided special school (GASS) supported by the Scottish government.
Local authorities from all over Scotland and the north of England refer pupils there and fund their placements.
The notice calling for an improvement plan within a week is the first of its kind to be issued for 15 years.
A report from Education Scotland last year criticised leadership at the school - and a follow up report said insufficient progress was being made putting things right.
The school has stressed its first priority is always the safety and wellbeing of pupils and a new principal was recently appointed.
Work is underway to come up with the improvement plan before the deadline.