So I'm using the "snaking" mod, and I had a fortress that had somewhat low production, and I wanted to improve it, but all the forest tiles were a bit far. So I started demolishing and rebuilding an improvement in order to extend the town as far as possible. Naturally I used the monument, because it's cheap to build.

As it turns out, however, every time I did this, my town gained another +1 to it's area of control. Before I realized what was happening, I had 1/4 of the map locked down, by just the one city.

So yeah, apparently if you demolish and rebuild the Monument improvement, it keeps giving you a bigger and bigger area of control. Tempted to try it with other improvements to see if it makes their benefits stack too...