There are a number of possible triples with Russia, thanks to Kaliningrad Oblast. You may with to exclude this, even though it is not an overseas territory, and it is an oblast (roughly, a state or province) of Russia.
- Russia, Poland, Belarus
- Russia, Poland, Ukraine
- Russia, Lithuania, Belarus
- Russia, Lithuania, Latvia
Another, possibly more "legitimate" answer not yet given is
- Tanzania, Malawi, Mozambique