Hmm, so how are you going to get all those national parliaments together?
If we go back to the early days of the European Parliament, it was the Parliamentary Assembly of the European Coal & Steel Community. Until the first direct elections of June 1979, Members of the European Parliament were members of national parliaments (MNPs) who were chosen to represent their nations.
One way forward could be to create a European Senate, with Senators chosen from among MNPs. These Senators would then be able to bring proposed European legislation to their legislatures for discussion, take soundings and report back, being accountable to the people via their national legislatures.
It would enable some MNPs to develop expertise in European matters, just as others develop expertise in other areas.
There should also be some form of flexibility about who Senators should be. For example, there would naturally be permanent-ish Senators, serving until their nation's next election, while there could be other ad hoc Senators, if, say, the Senate was going to discuss the Common Agricultural Policy, then some members of the House of Commons' Environment, Food & Rural Affairs Select Committee and the House of Lords' European Union Sub-Committee D could find themselves co-opted to go to Strasbourg to be Senators for those sessions.
Note that I said going to Strasbourg. One thing that annoys MEPs is the travelling circus, holding some sessions in Brussels and others in Strasbourg, with there being a Single Seat campaign. If a Senate were set up, then perhaps the French Government would agree to the Parliament always meeting in Brussels in return for the Senate being on French soil.
As for the size of the Senate, one choice is for each nation's Senate delegation to equal the number of votes a nation has in the Council of Ministers - ranging from 29 for Germany, France, the United Kingdom and Italy down to 3 for Malta. That makes 345 at the moment, although I expect Croatia, given its population, to have 7.
That gives us 352 Senators. If it is to take over some of the Council of Ministers' work, then it is sensible that something like Qualified Majority Voting is used. Either each national delegation decides among itself how it will cast the nation's vote(s) on a matter, or each Senator has one vote. Either way, a super-majority would be needed (maybe two-thirds, or 235 Senators) to pass anything coming to it from the Parliament.
This would bring national parliaments into the European legislative process at an earlier stage, and promote links between national parliaments and the European Parliament. In addition, it would make the Parliament think twice before legislating, as there would be the Senate hurdle to get over.