Sinn Féin finance spokesman Pearse Doherty has written to Central Bank Governor Philip Lane seeking the widening of the redress scheme after a High Court ruling, the Irish Independent has learned.
His letter to the Central Bank identifies policies sold by GE Money, Permanent TSB and Ulster Bank where he says more cases should be examined.
Payment protection insurance pays a policyholder's loan or credit card repayment if they become ill or unemployed.
But the insurance was sold to thousands of people who were ineligible - who would be unable to claim under the policies.
In 2011, the Central Bank told 11 financial firms to review sales of the product and pay back premiums and compensation.
Now Mr Doherty has written to the Central Bank pointing out that its review has missed out on thousands more policies.