In LotR the Two Towers, it is explained that Saruman has been kicked out of the Wizard council for allying with Sauron.
This allows Gandalf to become the new head of the order and become Gandalf the White. (I feel like this is what happened, but please correct me if I'm wrong).
I was under the assumption that each of the 5 Wizards had their own specific role to fulfil, each with their own purpose and power (hence why Gandalf could break Saruman's staff once he became the White Wizard, as Saruman was previously more powerful than him).
If this is the case, did anyone take up the mantle of the Grey Wizard? Or did a wizard need to die before he could return in another form?
Details from any canon would be appreciated.