Other than Kevin (you're right about him), I feel like all the characters had several focal traits, not just a one-dimensional schtick. They definitely refined and brought these to the forefront over time (especially right after season 1), but I don't feel like they ever got flat.
Also, a huge part of that show is the number of "main" characters, and seeing how those handful of traits among a large number of characters mix and mash and interact, both with each other, and in varying situations. I.e. Andy and Oscar may not be that complicated individually, but they hardly interacted until like season five and then suddenly got put in a situation or two together, which made for something fresh. That kind of thing happens constantly over the course of the show.