I managed to get a seven tile forest and there were three of the "gateway" improvements up for grabs. When the game started we'd decided that you can only buy any given improvement once, but the rules don't say either way.
Seems fair enough. Everything is open so opponents should try to prevent someone from getting so many points by getting 2 or more high value improvements.
Also, can you buy more than three improvements? If not, can you discard an improvement if you want to replace one?
Fair question. Although I can't imagine being able to spend 50% of your city actions acquiring improvements!