I'm again thinking of virtue: do Stoics consider that you can reach a state where you are virtuous, and therefore don't long for it any more?
I think that is a definite yes - when you get to the summit you are at the top and there is nothing greater.
I remember Emily Austin said that the Stoics didn't think anyone could really attain perfect virtue. The analogy was that you can drown just as easily in an inch of water as in the ocean: it's an all or nothing... And no one can be all virtuous all the time.
I think that's why the Christians allowed the Stoic strain to seep into their doctrines... We're all sinners. Even a little sin is still sin. Etc...