First, you will need to hit the final Milestone in your city's growth, Megalopolis. Exact population size required for this apparently depends on the map (for me it was 60,000, but I've heard conflicting accounts). This will also unlock Monuments.
While on the way, you can purchase new map tiles from Areas.
Note that nine tiles is the maximum size of your town, and you cannot own all of the tiles you can potentially choose at any point, so this might come as a surprise. Plan your tile purchases accordingly, so you don't end up with an awkward area.