Can you rebuild Capitols?

I imagine you could build a new capital in some other urban province...

More information here:

https://wiki.callofwar.com/wiki/PROVINCES

In a city click the contruction button, at the bottom of the buildings tab is a "special" section which you can build a new capital building.

If you've had a capital conquered it'll build a new one, otherwise it'll "move" your existing capital to the new city