Sinn Fein has called for the creation of nine new cross-border bodies and an expansion of existing organisations.
Sinn Fein said existing bodies should be expanded
They would be in addition to the six all-Ireland bodies set up by the Good Friday Agreement.
Sinn Fein wants extra bodies to cover justice, policing, social economy, energy, rural development, pollution control and mental health.
It has also called for communications and higher and further education bodies to be established.
Sinn Fein's John O'Dowd has warned the DUP that whether or not they meet the November deadline for restoring devolution, "there will be an expansion in the existing role of cross-border bodies".
Meanwhile, DUP Upper Bann MP David Simpson has said his party supports devolution in Northern Ireland that is "democratic, fair, accountable and free from the taint of terror and criminality".
"The people of Northern Ireland are not being served well by the continuance of direct rule."
He added: "Sinn Fein must face up to the difficult questions on criminality, decommissioning, disbandment and policing.
"There can, and will, be no tolerance of criminality and paramilitarism as far as participation in government is concerned," said Mr Simpson.