Which is exactly what we already have. There is what your local government says you should be doing, and there is what your friendly (or not so much) neighborhood superpowers say your government should be doing.
We also already have in most countries a hierarchy of governments - a state government, a central government, etc.
In the EU we certainly have regional government, member state government and EU institutions. All of these are different shades of government and in some cases conflict with each other.
In some areas EU has been a boon - a "safety valve" where the member state government is put into a competitive system where it has to align itself with external expectations from the EU institutions. I.e. breaking up their monopoly power in that sense.
Some national governments want/wanted to completely control the sale of medicine, foods, alcohol etc and to some extent EU has broken up that control.
