Yes great idea.
Rather than put the burden of building and updating stadiums and infrastructure like roads and rail on just one or two countries (like we had in Poland / Ukraine this year) you can spread it across many countries.
After all if two of the grounds were in say London and Paris for example, then it is quick for any team to fly from one to the other.
Quicker than flying from one side of Poland to the other side of Ukraine for a match for example like we had in Euro 2012.
Also major grounds like Wembley already have the facilties like airports nearby, hotels, rail links etc.
I have often thought the Olympics dont have to be in one country either. The horse events and the sailing for example were nowhere near London and could just as easily been in France or Holland or Belgium.
Instead of putting the huge cost on one country spread it across 3 or 4 countires, athletics on one country, swimming in another and so on.
Have one city as the main hosts, like London, but allow France or Holland to stage some events for example.