I think you can make a distinction between a single fat model (possibly named App or Application), and several fat models broken down into logical groups (Business, Customer, Order, Message). The latter is how I structure my apps, and each model roughly corresponds to a database table in a relational database or collection in a document database. These models handle all aspects of creating, updating, and manipulating the data that makes up the model, whether it is talking to the database or calling an API. The controller is very thinm responsible for little mor that calling the appropriate model and selecting a template.
