This talk will be about the block spin mean-field Potts model, in which the spins are divided into s blocks and can take q>1 different values (colors). Each block is allowed to contain a different proportion of vertices and behaves itself like a mean-field Ising/Potts model which also interacts with other blocks according to different temperatures. Of particular interest is the behavior of the magnetization, which counts the number of colors appearing in the distinct blocks. I will present central limit theorems for the magnetization in the generalized high temperature regime and show a moderate deviation principle for its fluctuations on lower scalings. We shall also compare our results to various related models and discuss open problems, which leave room for future investigations. This is joint work with Matthias Löwe and Holger Sambale.