The IHC has confirmed it is seeking leave to appeal against a court ruling that is its liable for millions of dollars in payments to staff.
The Court of Appeal last month ruled that workers on shifts requiring them to sleep overnight were entitled to backpay at the minimum wage rate instead of a much lesser allowance.
The IHC says it has filed leave to appeal with the Supreme Court.
The Government is the chief funder of the homes where the workers sleep over.
The Service and Foodworkers Union, which took the case on behalf of workers, says it will file papers to challenge the latest IHC move.