Probably. But the point is you can't do that in a binding way without having the national governments cede sovereignty through constitutional amendments, which instantly causes public uproar.
E.g. under the UK constitution (yes, the UK has a constitution, it is just not codified in a single act) the UK Parliament is sovereign, to the extent that it can not even bind future parliaments.
So without tricky constitutional changes (particularly tricky because parliament has pretty much "bootstrapped" its own constitutional powers in the UK into a position were giving them away again will need to be very carefully structured to stand up in court) it is pretty much impossible to grant the EU parliament any real power.
This is part of why the current structure of the EU uses a web of treaties to bind the executives of the member states in various to seek the passage of local laws to implement EU directives, with convoluted measures to cajole the national legislatives to follow through. It's still not ironclad - plenty of directives languish in national parliaments for years before being implemented (or get implemented with inconsistent differences in different member countries) exactly because the EU has very few means to push it through - but it's a far stronger method than trying to tie the national parliaments with no constitutional support.
E.g. under the UK constitution (yes, the UK has a constitution, it is just not codified in a single act) the UK Parliament is sovereign, to the extent that it can not even bind future parliaments.
So without tricky constitutional changes (particularly tricky because parliament has pretty much "bootstrapped" its own constitutional powers in the UK into a position were giving them away again will need to be very carefully structured to stand up in court) it is pretty much impossible to grant the EU parliament any real power.
This is part of why the current structure of the EU uses a web of treaties to bind the executives of the member states in various to seek the passage of local laws to implement EU directives, with convoluted measures to cajole the national legislatives to follow through. It's still not ironclad - plenty of directives languish in national parliaments for years before being implemented (or get implemented with inconsistent differences in different member countries) exactly because the EU has very few means to push it through - but it's a far stronger method than trying to tie the national parliaments with no constitutional support.