First, it is the Federation Fleet that expands its territory; private powers do not possess this ability.
The Federation Fleet constantly expands, exploring neighboring civilizations or seeking mineral-rich resource stars and habitable planets.
When they find a planet with signs of life,
if it is suitable for habitation and has a long life expectancy, the Federation will send people to eliminate life on the planet and then pull it back into the Federation's territory using a tractor beam, inviting companies to develop infrastructure on it.
Favorable policies would be provided.
For example, tax exemption for ten years, priority in purchasing land, exclusive supply of certain goods, etc.
At the same time, part of the Federation's citizens would be encouraged to migrate to this planet, and they would receive good policies, such as having their children's household registration on the planet, which would give them extra points when applying for university.
Just like that.