To feel deep, a character needs to show up in multiple roles

I suspect that to feel deep, a character needs to show up in multiple roles in their story. I mean roles in the broadest possible sense: "mother," "daughter," "sister," "annoying {older, younger} sister," "thoughtful {older, younger} sister," "weeb," "superhero," "supervillain," "pushy salesperson," et cetera. They need to say different things at different times for different reasons. If they always show up and play the same role—it's bound to feel stiff, however interesting that role is.

Is that true? It seems to explain one character I find disappointing—because she's not explored in enough depth. Are there counterexamples?

Does Gandalf show up in multiple roles? He's nearly always the solemn wise wizard. But sometimes he's the cheerful mysterious wizard, or the powerful dangerous wizard. Once or twice I think he even shows up as a concerned friend—for example, while visiting Bilbo. So I think it does hold somewhat for Gandalf. This feels like cheating—most of these roles are some variation on "{adjective} {adjective} wizard." Are those really meaningfully distinct roles? I think the wizard vs. concerned friend distinction is true and important, though. So maybe you don't need them to show up in very many distinct roles—two might be enough.