One component library with multiple styles

I’m currently setting up new libraries and I created a component library with a generic style and, separately, multiple style libraries with colors/fonts for different clients.

Once I start a new project the idea is to use the component library and select the style library to the specific client.

However, every time I’m adding a new component, it comes with the generic style of the component library and I need to keep doing “swap library” to have the correct style. Is it possible to “force” the style in that document in a way that every time I’m adding a component to the comes it already comes with the style I need?

Is there a better way to do this?