Depending on your nationality, a lot of countries have flexible tourist visas. For example, Americans can visit Armenia for 6 months, Albania for 12 months, Georgia for 12 months, India for 6 months at a time (up to 10 years), and so on.

In Europe, you also have many countries outside of the Schengen area, meaning that you can do three months in one then hop to another. E.g. spend 3 months in Berlin, then 3 months in Kyiv, then 3 months in Paris, then three months in Belgrade.