Panini does the bigger binders for the PL, La Liga & Serie A.
Outside the UK it's the same with the Panini Premier League binders.
Only in the first season Panini had the big binders in the rest of Europe. After that only half the size.
Due to Panini's geo-restrictions, it is unfortunately not as easy to order everything from everywhere in Europe. Fortunately, Topps offers more options, but Brexit and import duties have made everything much more expensive than it used to be.
With the Panini collections, due to the mass of Limited Edition Cards, it is almost impossible to do otherwise than to store them in an extra folder or extra pages, as you described (In the meantime I see the Panini Limited Editions as an extra collection, due to the quantity and therefore I have no problem with putting them in an extra binder)
The situation is different with the current collection from Topps, where someone simply didn't think along, since it was pretty clear in advance how many cards were still to appear and that, if you take this into account, it is impossible to fit everything (what is part of the collection) in a small binder.