Yes, you can!
But you have to log out of the first account and remove all data as accessing an existing village with a new account will bind that village to the account instead of creating a new one.
So, how do I do it?
Simply log out of your current Game Center account and uninstall Clash of Clans, as this removes all village and device identification numbers.
After that, log into a new Game Center account and reinstall/open the game.
Note: If you have already have a village and accidentally opened it with a new account, that account will have that village also bound to it. In this case, you'll need to create another Game Center account.
So, if I wanted to switch back to my old village, can I?
Yes, and you don't need to reinstall. Just open Clash of Clans logged into the new account and it'll ask you whether you would like to switch villages. In this case, select Yes.