This is wild, but what about...
A league (cup) where the champion of each country ( even the "smaller" leagues: Ireland, scotland, Iceland, Italy ect

) plays the old style knock out, no groups, just home and away.
Have a second much larger competition, the size of the champions league now, with the best of the rest of Europe - say 5 teams from the biggest leagues, filtering down ect.
Now, as the teams from the first "Champions" league get knocked out, they drop into the other competition - much like the system now with the CL & the Europa - except.. except, dropping into this second tournament wouldn't be a shitt tournament, and one worth competing in..
Ahh forget it.