It's possible when you have friendly Civs, but if the Civ leader has 'backstabbing' rating high in it's flavors (like Oda, Alex, Monty) they will probably attack you unless you have a strong, up-to-date army.
But with leaders like Kamehameha and Wu Zetian it's no problem, there are trusty ones too. Of course if you go on city-state conquering spree or make friends with tyrants even the more mellow ones might ally against you..
With the upcoming expansion on spring, the religion and ideologies of Civs are said to be big modifiers with some Civs, I like that.