Yes, there are many non-EU countries that would stamp my passport, but we try to avoid flying and, having a home in France, we go there quite a lot and otherwise take trains around Europe. There is so much to see there and sun, sea and sand, feature pretty low on my list of holiday requirements. So for the last 30 years, stamps have been few and far between on my passport. Now i am going to get 16 to 20 just going to and from France
When the passport fills, I think you send it back and the passport agency add extra pages.