Advance on the tech tree. Some techs reward with an expansion (that you need to pay for), and going up an era open up two more diamond expansions.
Advance on the contentment. Some Provinces give the reward of an expansion (that you need to pay for)
Earn Medals, there are a series of expansions that can be bought with medals. You earn medals in the PvP towers for top places, Donating to Great Buildings (top donors get medals) and from some special buildings.