A distinction based on age. Different pronouns for children, adults, elderly or relative to the speaker's age.
That's the one I thought about after posting.
A distinction based on status and respect. A bit similar to what Japanese does with honorific name suffixes but in pronoun form.
It could actually be the evolved version of the age-based pronouns. The pronouns for older people become the pronouns for respectable individuals and stuff like that.
A distinction based on proximity. One set of pronouns for a person near the speaker, one for a person near the listener and one for a person somewhere else. Japanese does something similar for things (これ kore, それ sore, あれ are) but as far as I know, not for people.
A distinction based on familiarity. One set of pronouns to refer to close friends and family, one for acquaintances, one for strangers.
I like these weirdly practical pronouns! I can imagine them in a language of a highly rational alien species.
One of the conlangs I'm occasionally working on has pronouns based on the shortened form of names: the first syllable of the person's name plus a suffix. Plus one set of pronouns for if you don't know (or don't want to mention) a person's name.
I'd argue that shortened names aren't pronouns. Like, "Bob" isn't a pronoun after all. But that's a cool idea nonetheless.