Gardening. Lots of Gardening. Oh dear god the gardening!!!
hehe, anyyyway... yeah preety much anything except suicidal stuff. They get a new saving throw every time you tell them to do something that's "against their nature"
So telling a paladin to go kill a balor, or asking a back-stabbing sneaky thief that would turn his own mother in info about his "friends" then those in my mind should be automatic.
As far as multiple saves go, I would only allow them if your severity of actions really went up.
For example, you have one of the pcs captured and you've dominated him. If your asking him questions about the other pcs, and he's generally doesn't want the party dead (hey, you never know) then he would get a save. He fails, so you can ask him all the questions in the world. Now, you ask him to kill the party, that would be another save.
If your doing this to players, and they start whining about (oh, I should get a new save for that, I should get a new save for this!!) remind them that they only have to follow the strict letter of the orders given, they can work around their orders. That's a whole lot more fun imho, then sitting there thinking up excuses to bust out of domination.