Furious parents are demanding further action at Liverpool's Alder Hey Children's Hospital after the chair was asked to leave last week.
Families say repeated mistakes have been made in returning part of a collection of 2,000 organs for burial.
Junior health minister Lord Hunt told trust chair Frank Taylor to step down after the hospital admitted it had 'mistakenly disposed of ' organs which were due to be given to the family of Stephen White. Lord Hunt is now studying a report on the case. But Ian Cohen, solicitor for the Pity II parents' support group, said it was not an isolated incident. 'We are aware of at least one other case where organs have been disposed of after September 1999, '(when the collection was revealed).
Stephen's family had been planning to bury his heart, brain and lungs last week, eight years after he died.
Mr Cohen claimed that mistakes included mixing up a child's date of death with its mother's date of birth and getting the names on caskets containing returned organs wrong.
Hospital staff had also taken 'fresh samples' from organs they were supposed to give to bereaved parents.
Mr Cohen said: 'I am not looking for anyone in particular to lose their job, but what I am looking for is accountability.
'If that means someone else has to leave their job to restore confidence , then so be it. '
The trust is already facing an independent investigation into its collection of organs, first revealed in evidence to the Bristol Royal Infirmary inquiry.
It heard that up to 15,000 children's and adults' hearts had been kept by hospitals in England and Wales.
Trust chief executive Hilary Rowland met Stephen White's parents to explain the disposal of his organs and said: 'We deeply regret the distress that this has caused to the family and we sympathise with them in their grief. '
A spokesperson for the NHS Executive North West regional office said further resignations were not immediately expected.
'The feeling is that the management team has had a very difficult case to deal with. Inevitably there will be some mistakes. '
No acting chair has yet been chosen, but an appointment is expected by tomorrow.