As it is not going to happen I can only give my view on how it could.
A system of regional Parliaments subordinate to the EU parliament. They don't have to be based on nations, they could be based on regions within current national boundaries. Like a regional Parliament for NW England or even Greater Manchester. The more democracy the better in my view.
By centralising power, you could actually decentralise power and introduce more localism that can adapt to the needs of the locale.
I don't think the current structure of the EU is fit for purpose, I don't think anybody leave or remain does, it definitely needs a thorough overhaul and it needs to be more democratic and more representative.