Knight, what you are talking about isn't personality. Personality is about how people perceive the world and make decisions. E.g Spock = logic, McCoy = feelings etc.
You mean characters with different motivations. E.g. you could have a Vulcan who uses the same though processes as Spock, but uses them for a different purpose. E.g. the *evil* Spock in the mirror universe uses the same kind of logic as Spock, yet his aims are slightly different.