BRISBANE, Nov 14 - The Presbyterian and Methodist School's Authority is under heavy fire from the Somerville House Parents & Friends aligned group Beyond PMSA, which is outraged by the governing body's management.

Somerville principal Florence Kearney, other senior staff and school council members have all resigned in recent months in opposition to the PMSA, which also oversees three other prominent Queensland schools.

The dramas were sparked when Somerville House senior executive Rick Hiley was axed by Kearney over an alleged IT data breach but then promoted by the PMSA to become their executive manager, effectively overseeing the school's governance.

Protestors dressed in green - the school's colours - will gather at Speaker's Green outside Parliament House from 7.30am on Tuesday.

It follows an initial street protest outside Somerville House three weeks ago, while many parents have chosen to take their daughters out of the school since.

A Beyond PMSA spokeswoman said the organisation was not going away or going to be quiet.

"Since our last rally, Beyond PMSA has grown in strength with more revelations about the mismanagement and cover-ups of the PMSA," she said in a statement on Monday.

The spokeswoman said the church moderators' announcement on Friday that former federal court judge Richard Chesterman had been appointed to "promote healing" between the PMSA and Somerville House was inadequate.

"This completely fails to acknowledge the debacle they have on their hands, the future direction the parents want the schools to take, and the depth of anger they have towards the PMSA," she said.